TY - JOUR. T1 - In vitro packaging of a λ Dam vector containing EcoRI DNA fragments of Escherichia coli and phage P1. AU - Sternberg, Nat. AU - Tiemeier, David. AU - Enquist, Lynn. PY - 1977/5. Y1 - 1977/5. N2 - In this report we describe a coliphage λ vector system for cloning endo R. EcoRI DNA fragments. This system differs significantly from those previously described in two ways. First, restricted and ligated DNA is encapsidated in vitro. Second, with increasing λ DNA size in the range 78 to 100% that of wild-type, the efficiency of DNA encapsidation into infectious phage particles markedly increases. For λ wild-type DNA the efficiency of in vitro packaging (106 to 107 plaques produced per μg of added DNA) is equal to, or better than, the standard CaCl2 transfection method. The use of a Dam mutation to facilitate recognition of size classes of inserted fragments is described. Using this vector and in vitro packaging, several E. coli and phage P1 endo R.EcoRI fragments were ...

documentclass{article} \usepackage{newtxtext,newtxmath} \usepackage{amsmath} \DeclareMathOperator{\sn}{sn} \DeclareMathOperator{\cn}{cn} \DeclareMathOperator{\dn}{dn} \begin{document} \begin{equation} \begin{gathered} \omega^3x_{4}(s) = \begin{minipage}[t]{.7\displaywidth} \raggedright\linespread{1.2}\selectfont \begin{math} x_4(\varphi_0) -2 \cos^3 ( \phi )sk^2 +2k^2x_1(\varphi_0) \cos^2( \phi ) +4 \cos^3 ( \phi )E ( s ) k^2+x_3(\varphi_0)\sin ( \phi ) s - \cos^3( \phi ){s}^2E( s ) +2 \cos^3 ( \phi )s ( E (s) ^2 +\cos ( \phi ) {s}^2E ( s ) - 2x_3(\varphi_0)\sin ( \phi ) E ( s ) -1/6\cos ( \phi ) {s}^3-4/3 \cos^3 ( \phi ) E ( s ) ^3 -1/2 x_1(\varphi_0) \cos^2 ( \phi ){s}^2-2 x_1(\varphi_0) \cos^2 ( \phi ) E ( s ) ^2 -2\cos ( \phi) s E ( s ) ^2 -2x_1(\varphi_0)sE( s ) + k\sin (\phi ) \cn(s) {s}^2 \cos^2( \phi ) +2 \cos^3 ( \phi )sk^2 \sn(s) ^2 -2/3\cos ( \phi) E ( s) +4/3k^3\cn(s) \sn(s) ^2\sin( \phi ) \cos^2 ( \phi )+2k\sin ( \phi ) \cn(s) +2/3\cos ( \phi ) s-8/3\cos ( \phi ) k^2\dn (s) \sn(s) ...

4DQJ: Selective pressure causes an RNA virus to trade reproductive fitness for increased structural and thermal stability of a viral enzyme.

4DQJ: Selective pressure causes an RNA virus to trade reproductive fitness for increased structural and thermal stability of a viral enzyme.

The objective of this study is to evaluate the safety and utility of bacteriophage phi X174 immunization as a tool to assess the immune competence of HIV-infected patients at different stages of disease in vivo, and to assess the impact of viral load levels and therapy-induced changes in viral load levels on the response to immunization with the neo-antigen bacteriophage phi X174. Bacteriophage phi X174 immunization is a method that has been in use for more than 25 years to assess the immunity of patients with various types of primary and secondary immunodeficiencies, including 48 HIV-infected patients. This is a prospective open-label, controlled study which will enroll 39 HIV-infected patients and 13 healthy volunteers, male or female with 18 years of age and over. The HIV-infected patients will be divided into 3 groups according to their CD4 cell count: less than 200 cells/mm(3), between 200 and 500 cells/mm(3) and greater than 500 cells/mm(3). After screening and a two week pre-study ...

Many viruses package their genome into preformed capsids using packaging motors powered by the hydrolysis of ATP. The hexameric ATPase P4 of dsRNA bacteriophage phi12, located at the vertices of the icosahedral capsid, is such a packaging motor. We have captured crystallographic structures of P4 for all the key points along the catalytic pathway, including apo, substrate analog bound, and product bound. Substrate and product binding have been observed as both binary complexes and ternary complexes with divalent cations. These structures reveal large movements of the putative RNA binding loop, which are coupled with nucleotide binding and hydrolysis, indicating how ATP hydrolysis drives RNA translocation through cooperative conformational changes. Two distinct conformations of bound nucleotide triphosphate suggest how hydrolysis is activated by RNA binding. This provides a model for chemomechanical coupling for a prototype of the large family of hexameric helicases and oligonucleotide translocating

During the replication cycle of double-stranded (ds) RNA viruses, the viral RNA-dependent RNA polymerase (RdRP) replicates and transcribes the viral genome from within the viral capsid. How the RdRP molecules are packaged within the virion and how they function within the confines of an intact capsid are intriguing questions with answers that most likely vary across the different dsRNA virus families. In this study, we have determined a 2.4 Å resolution structure of an RdRP from the human picobirnavirus (hPBV). In addition to the conserved polymerase fold, the hPBV RdRP possesses a highly flexible 24 amino acid loop structure located near the C-terminus of the protein that is inserted into its active site. In vitro RNA polymerization assays and site-directed mutagenesis showed that: (1) the hPBV RdRP is fully active using both ssRNA and dsRNA templates; (2) the insertion loop likely functions as an assembly platform for the priming nucleotide to allow de novo initiation; (3) RNA transcription ...

iframe src=https://biblio.ugent.be/publication?q=keyword+exact+%22DOUBLE-STRANDED-RNA%22&embed=1&hide_pagination=1&hide_info=1&hide_options=1&hide_cluster=1 ...

of phi and psi for randomly chosen residues; these values range from -98° to -178° and from +90° to +167°, respectively. These ranges overlap the values for the twisted parallel showing that there is no differences in the ranges for the two types of twisted sheets. Median values for phi and psi are -125° and +140°, respectively. ...

Aims: To develop infectious (live/dead) enveloped virus test indicators and response surface methodology (RSM) models that evaluate survival of an enveloped ribonucleic acid (RNA) virus on contaminated aircraft materials after exposure to hot, humid air (HHA).Methods and Results: Enveloped RNA bacteriophage Phi6 (Φ6) was dried on wiring insulation, aircraft performance coating (APC), polypropylene, and nylon at ≥ 8 log10 plaque-forming units (PFU) test coupon−1. Only 2.4 log10 inactivation was measured on APC at 70°Celsius (°C), 5% relative humidity (RH) after 24 h. In contrast, HHA RSM models showed a 90% probability of a 7 log10 inactivation at ≥63°C, 90% RH after 1 h, and decontamination kinetics were similar across different materials. HHA decontamination of C-130 and C-17 aircraft showed >7 log10 and ≥5.9 log10 inactivation of enveloped virus on 100 and 110 test indicators, respectively, with a 1-h treatment, excluding ramp-up and ramp-down times.Conclusions: Enveloped RNA virus test

PubMed comprises more than 30 million citations for biomedical literature from MEDLINE, life science journals, and online books. Citations may include links to full-text content from PubMed Central and publisher web sites.

NIH thinks that a biological motor from bacteriophage phi29 indeed has a potential for the future of nanomedicine, for a number of reasons. The press offic

Virus particles Monoliths Ion exchang echromatography Virus purification Bacteriophage PRD1 Bacteriophage phi05_2302

Viral structure Virus: poison (Latin); infectious particles consisting of a nucleic acid in a protein coat Capsid; (viral envelopes); DNA or RNA Bacteriophages (phages)

In mathematics, the Crofton formula, named after Morgan Crofton (1826-1915), is a classic result of integral geometry relating the length of a curve to the expected number of times a random line intersects it. Suppose γ {\displaystyle \gamma } is a rectifiable plane curve. Given an oriented line l, let n γ {\displaystyle n_{\gamma }} (l) be the number of points at which γ {\displaystyle \gamma } and l intersect. We can parametrize the general line l by the direction φ {\displaystyle \varphi } in which it points and its signed distance p {\displaystyle p} from the origin. The Crofton formula expresses the arc length of the curve γ {\displaystyle \gamma } in terms of an integral over the space of all oriented lines: length ( γ ) = 1 4 ∬ n γ ( φ , p ) d φ d p . {\displaystyle {\text{length}}(\gamma )={\frac {1}{4}}\iint n_{\gamma }(\varphi ,p)\;d\varphi \;dp.} The differential form d φ ∧ d p {\displaystyle d\varphi \wedge dp} is invariant under rigid motions, so it is a natural ...

This collection from the Belgian Nuclear Research Centre (SCK.CEN) provides historical reference plasmids for various incompatibility families. The collection also includes a set of bacterial host strains meant for cloning and in vitro packaging of and/or working with phages.

Hi, When I was in Japan, I used ETHACHINMATE as a carrier to recover DNA (from WAKO JUNYAKU Co.). In their catelogy, they show some data glycogen has effect on transformation efficency, but ethachinmate does not. I dont know whether linar polyacrylamide effect transformation and in vitro Packaging efficiency. Huang ...

An interesting number and sequence Phi What is Phi? Phi ( = 1.618033988749895... ), most often pronounced fi like fly , is simply an irrational number like pi ( p = 3.14

Phi Việt Karaoke 06: Volume 06 - Mưa Bụi 01. Neu Anh Dung Hen - Unknown 02. Ke Co Don - Unknown 03. Doan Cuoi Tinh Yeu - Unknown 04. Hoa Bien - Unknown 05. Mot Minh Thoi - Unknown 06. Mong Chieu Xuan - Unknown 07. Nang Ha - Unknown 08. Viet Tu K. B. C - Unknown 09. Mong...

The key to truly high performance with the Phi coprocessor is to express sufficient parallelism and vector capability to fully utilize the device. Here is a timing framework that enables you to measure and optimize performance and push it past 1 teraflop.

The key to truly high performance with the Phi coprocessor is to express sufficient parallelism and vector capability to fully utilize the device. Here is a timing framework that enables you to measure and optimize performance and push it past 1 teraflop.

TY - JOUR. T1 - High efficiency, restriction-deficient in vitro packaging extracts for bacteriophage lambda DNA using a new E.coli lysogen. AU - Gunther, Edward. AU - Murray, Noreen E.. AU - Glazer, Peter M.. PY - 1993/8/11. Y1 - 1993/8/11. UR - http://www.scopus.com/inward/record.url?scp=0027236017&partnerID=8YFLogxK. UR - http://www.scopus.com/inward/citedby.url?scp=0027236017&partnerID=8YFLogxK. U2 - 10.1093/nar/21.16.3903. DO - 10.1093/nar/21.16.3903. M3 - Article. C2 - 8396240. AN - SCOPUS:0027236017. VL - 21. SP - 3903. EP - 3904. JO - Nucleic Acids Research. JF - Nucleic Acids Research. SN - 0305-1048. IS - 16. ER - ...

These pages were created in support of the dsRNA Virus Symposia. The editors also wish to acknowledge continuing support from BBSRC, DEFRA and the Commission of the European Community. ...

Distinguishing features. See discussion under family properties. Virion See discussion under family properties. Genome organisation and replication. See discussion under family properties. Biology. See discussion under family properties. Species demarcation criteria. Not currently defined. ...

The absolute requirement for primers in the initiation of DNA synthesis poses a problem for replicating the ends of linear chromosomes. The DNA polymerase of bacteriophage phi29 solves this problem by using a serine hydroxyl of terminal protein to prime replication. The 3.0 A resolution structure sh …

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First case you have: $$T=\frac 12 M\,v^2+\frac 12 I\omega^2=F\,L$$ with : $$v=\omega\,R~,I=\frac 12 M\,R^2$$ you obtain $$ \omega=\frac{2}{3}\frac{\sqrt{3}}{R}\,\sqrt{\frac{F\,L}{M}}$$ second case $$T=\frac 12 M\,v^2+\frac 12 I\omega^2=F\,L+F\,R\,\varphi$$ with $$\varphi=\frac{x}{R}=\frac{L}{R} \,,v=\omega\,R$$ you obtain $$ \omega=\frac{2}{3}\frac{\sqrt{6 ...

Book now at Lucy Restaurant and Bar at Bardessono in Yountville, CA. Explore menu, see photos and read 1103 reviews: We are locals and have been coming to Lucy periodically for years; we have had both good and poor experience mostly related to service. Todays visit ...

TY - JOUR. T1 - Optimization of the in vitro packaging efficiency of bacteriophage T7 DNA. T2 - effects of neutral polymers. AU - Son, Marjatta. AU - Hayes, Shirley J.. AU - Serwer, Philip. PY - 1989/10/30. Y1 - 1989/10/30. N2 - The in vitro DNA packaging of several DNA bacteriophages is stimulated by the presence of neutral polymers. To optimize bacteriophage T7 DNA packaging and to understand the basis for optimization, the efficiency ofT7 DNA packaging has been determined at completion, as a function of the type, molecular mass, and concentration of the polymer added. When the polymer used was polyethylene glycol (PEG) of 0.2, 0.6 or 12.6 kDa, the efficiency of DNA packaging reached maximum at an intermediate concentration of polymer. The osmotic pressure (Pos) at maximum efficiency was either in, or close to, the range of colloid Pos measured for the intact host cell. The optimum Pos increased as the size of the polymer used decreased. PEG-100 (of 0.1 kDa) did not stimulate in vitro T7 DNA ...

TY - JOUR. T1 - Optimization of the in vitro packaging efficiency of bacteriophage T7 DNA. T2 - effects of neutral polymers. AU - Son, Marjatta. AU - Hayes, Shirley J.. AU - Serwer, Philip. PY - 1989/10/30. Y1 - 1989/10/30. N2 - The in vitro DNA packaging of several DNA bacteriophages is stimulated by the presence of neutral polymers. To optimize bacteriophage T7 DNA packaging and to understand the basis for optimization, the efficiency ofT7 DNA packaging has been determined at completion, as a function of the type, molecular mass, and concentration of the polymer added. When the polymer used was polyethylene glycol (PEG) of 0.2, 0.6 or 12.6 kDa, the efficiency of DNA packaging reached maximum at an intermediate concentration of polymer. The osmotic pressure (Pos) at maximum efficiency was either in, or close to, the range of colloid Pos measured for the intact host cell. The optimum Pos increased as the size of the polymer used decreased. PEG-100 (of 0.1 kDa) did not stimulate in vitro T7 DNA ...

This site is supported by the Association of Applied Biologists. It was developed and maintained for many years by scientists at Rothamsted Research: John Antoniw (software, databases and web) Mike Adams (taxonomic and sequence data). This project was rebuilt by Xoons Ltd.. ...

Optimize performance while maintaining a unified hardware and software environment with the latest products from the Intel® Xeon Phi™ processor family

Do your feet cry out in pain at the end of the day? Is it sometimes difficult to stand at all because the burning is unbearable? I want to help you find the

Cystovirus is a genus of viruses, in the family Cystoviridae. Pseudomonas syringae pathovar phaseolicola bacteria serve as natural hosts. There is currently only one species in this genus: the type species Pseudomonas phage phi6. Group: dsRNA Order: Unassigned Family: Cystoviridae Genus: Cystovirus Pseudomonas phage phi6 Pseudomonas phage phi8 Pseudomonas phage phi12 Pseudomonas phage phi13 Pseudomonas phage phi2954 Pseudomonas phage phiNN Pseudomonas phage phiYY Cystoviruses are distinguished by their tripartite dsRNA genome, totaling ~14 kb in length and their protein and lipid outer layer. No other bacteriophage has any lipid in its outer coat, though the Tectiviridae and the Corticoviridae have lipids within their capsids. Most identified cystoviruses infect Pseudomonas species, but this is likely biased due to the method of screening and enrichment. The type species is Pseudomonas phage phi6, but there are many other proposed members of this family. Pseudomonas phage φ7, φ8, φ9, φ10, ...

Author Summary The fitness effects of mutations are the raw material for natural selection. It has been shown that point mutations typically have strongly deleterious effects in plant and animal RNA viruses, whereas cellular organisms are comparatively more robust. Here, we characterize the fitness effects of random mutations in DNA viruses and compare them with those found in RNA viruses, using six phage species of similar genome sizes. To achieve this goal, we introduced mutations by chemical and site-directed mutagenesis, identified the genetic changes by sequencing, and quantified their fitness effects using growth-rate assays. In all cases, mutations had a strong average impact on fitness. We conclude that mutational sensitivity is a general property of viruses with small genomes and discuss the evolutionary implications of these findings.

Characterizing the genome of mature virions is pivotal to understanding the highly dynamic processes of virus assembly and infection. Owing to the different cellular fates of DNA and RNA, the life cycles of double-stranded (ds)DNA and dsRNA viruses are dissimilar. In terms of nucleic acid packing, dsDNA viruses, which lack genome segmentation and intra-capsid transcriptional machinery, predominantly display single-spooled genome organizations1-8. Because the release of dsRNA into the cytoplasm triggers host defence mechanisms9, dsRNA viruses retain their genomes within a core particle that contains the enzymes required for RNA replication and transcription10-12. The genomes of dsRNA viruses vary greatly in the degree of segmentation. In members of the Reoviridae family, genomes consist of 10-12 segments and exhibit a non-spooled arrangement mediated by RNA-dependent RNA polymerases11-14. However, whether this arrangement is a general feature of dsRNA viruses remains unknown. Here, using cryo-electron

Populations are at risk of extinction when unsuitable or when sink habitat exceeds a threshold frequency in the environment. Sinks that present cues associated with high-quality habitats, termed ecological traps, have especially detrimental effects on net population growth at metapopulation scales. Ecological traps for viruses arise naturally, or can be engineered, via the expression of viral-binding sites on cells that preclude viral reproduction. We present a model for virus population growth in a heterogeneous host community, parameterized with data from populations of the RNA bacteriophage Φ6 presented with mixtures of suitable host bacteria and either neutral or trap cells. We demonstrate that viruses can sustain high rates of population growth in the presence of neutral non-hosts as long as some host cells are present, whereas trap cells dramatically reduce viral fitness. In addition, we demonstrate that the efficacy of traps for viral elimination is frequency dependent in spatially ...

The IUPHAR/BPS Guide to Pharmacology. PHI ligand page. Quantitative data and detailed annnotation of the targets of licensed and experimental drugs.

pHI, MY 3 1/2 YEAR OLD SON HAS PA.WE FOUND OUT WHEN HE WAS 2.I HAVE READ SEVERAL ARTICLES SAYING THAT IF YOU ARE NOT EXPOSED TO PEANUTS FOR 2-4 YEARS

Comparisons of Y-chromosome sequences in various mammals reveal abundant gene loss early in the chromosomes evolution but remarkable gene stability across the Y chromosomes of extant species. See Articles p.488 & p.494 Mammalian Y chromosomes, known for their roles in sex determination and male fertility, often contain repetitive sequences that make them harder to assemble than the rest of the genome. To counter this problem Henrik Kaessmann and colleagues have developed a new transcript assembly approach based on male-specific RNA/genomic sequencing data to explore Y evolution across 15 species representing all major mammalian lineages. They find evidence for two independent sex chromosome originations in mammals and one in birds. Their analysis of the Y/W gene repertoires suggests that although some genes evolved novel functions in sex determination/spermatogenesis as a result of temporal

Bacteriophages are perceived to be good models for the study of airborne viruses because they are safe to use, some of them display structural features similar to those of human and animal viruses, and they are relatively easy to produce in large quantities. Yet, only a few studies have investigated them as models. It has previously been demonstrated that aerosolization, environmental conditions, and sampling conditions affect viral infectivity, but viral infectivity is virus dependent. Thus, several virus models are likely needed to study their general behavior in aerosols. The aim of this study was to compare the effects of aerosolization and sampling on the infectivity of five tail-less bacteriophages and two pathogenic viruses: MS2 (a single-stranded RNA [ssRNA] phage of the Leviviridae family), F6 (a segmented double-stranded RNA [dsRNA] phage of the Cystoviridae family), FX174 (a single-stranded DNA [ssDNA] phage of the Microviridae family), PM2 (a double-stranded DNA [dsDNA] phage of the ...

The importance of the P3 protein in host switching events in phage ϕ6 has been previously established [36, 45]. This study confirmed this observation, but additionally brought to light the importance of the P12 protein in host switching events. This non-structural protein controls the liberation of mature ϕ6 particles from the host cytoplasmic membrane, but is not incorporated into the virion [46]. Like many eukaryotic viruses, Cystoviridae have envelopes comprised of both viral proteins and host lipids. Different hosts may have different lipid constituents which are contributed to the viral envelope and thus may require slightly altered P12 proteins for efficient envelope assembly. We have already shown that phage ϕ6 maturation in ERA affects fitness when the virion infects PP, and vice versa[25, 36]. We assume this epigenetic effect is mediated by the lipids taken from these very different hosts, and we speculate that our current results may relate to the importance of host lipid ...

Price: 1949.00 THB. Phi Phi, Bamboo, Maiton: ThePhi Phi Islandsare the best known of the Andaman Islands Phi Phi Island Tour will take you to all the best and most famous beaches on the Phi Phi Islands Youll have time to snorkel and just soak in the glorious views The coral reefs at Phi Phi Islands are very close to the beach so you can just snorkel with the kit included in the Phi Phi Tour price and get to see some of the most amazing colours you will ever see

A selection of pictures of Koh Phi Phi, twin islands lying about half-way between Krabi and Phuket in the Andaman sea off Southern Thailands west coast. Of these two islands only the larger, Koh Phi Phi Don, a dumbbell shaped slice, is inhabited. The smaller one, Koh Phi Phi Leh, is a popular destination for day trips from either Phuket or Koh Phi Phi Don. Only Loh Dalam bay on Koh Phi Phi Don is really suitable for swimming as the other bay is used as a harbour for boats and ships ...

MUSIC] The computation of added stiffness is easy because it only depends on some integrals over the interface. To compute the added mass we have to go a bit further. The added mass m A was defined as the inertia coefficient, when we obtained the force acting on the solid. It is made of the mass number, M, and of the sum of an interface of quantities that we know. Normal n, mode shape of the solid motion phi, and a quantity that we have to compute, the pressure shape, phi p. What is phi p? It was related to the velocity shape Phi u through phi u equals minus grad of phi p, and phi u was the solution of div of phi u equals zero, and phi u n equals phi n, at the interface. By taking the divergence of this momentum equation, we have div of grad of phi_p equals zero. So, we just have to find the field phi p, that satisfies Laplace equation, delta of phi p. equals zero, with a boundary condition at interface. Once we have phi p, we will obtain the added mass ma by a simple sum of the interface. ...

TABLE-US-00028 2005 IBM neigbors chr. 10 10 10 11 11 11 11 2005 IBM neigbors sample position 261 290 290 1 1 2 2 No sample su1 se phi062 phi323152 phi323152 phi101249 phi101249 Phi346482 Phi346482 1 017 n n 160 137 137 -- -- 119 119 2 044 n n 160 137 137 -- -- 119 119 3 006 n p 160 137 137 -- -- 119 119 4 007 n p 160 134 134 -- -- 119 119 5 009 n p 160 137 137 -- -- 119 119 6 047 n p 160 137 137 -- -- 119 119 7 637 n p 160 137 137 -- -- 119 119 8 001 p n 160 137 137 -- -- 119 119 9 046 p n 160 137 137 -- -- 119 119 10 048 p n 160 137 137 -- -- 119 119 11 049 p n 160 137 137 -- -- 119 119 12 109 p n 160 137 137 -- -- 119 119 13 354 p n 160 137 137 -- -- 119 119 14 sh2-i n n 158 135 135 141 141 119 119 2005 IBM neigbors chr. 11 11 11 11 11 11 2005 IBM neigbors sample position 3 3 4 4 5 5 No sample Phi213398 Phi213398 phi109624 phi109624 Phi159819 Phi159819 1 017 302 302 131 131 125 125 2 044 302 302 131 131 125 125 3 006 302 302 140 140 125 125 4 007 302 302 140 140 125 125 5 009 302 302 131 131 ...

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Measurements of differential cross sections d sigma/d phi* and double-differential cross sections d(2)sigma/ld phi*d/y/ for inclusive Z boson production are presented using the dielectron and dimuon final states. The kinematic observable phi* correlates with the dilepton transverse momentum but has better resolution, and y is the dilepton rapidity. The analysis is based on data collected with the CMS experiment at a centre-of-mass energy of 8 TeV corresponding to an integrated luminosity of 19.7 fb(-1). The normalised cross section (1/sigma) d sigma/d phi*, within the fiducial kinematic region, is measured with a precision of better than 0.5% for phi* , 1. The measurements are compared to theoretical predictions and they agree, typically, within few percent ...

Adventure, Excitement, Exploration. This is what Phi Phi Islands are. All 4 Diving Phuket Thailand invite you to paradise for an unforgettable adventure.

with(numtheory): A000029 := proc(n) local d, s; if n = 0 then RETURN(1); else if n mod 2 = 1 then s := 2^((n-1)/2) else s := 2^(n/2-2)+2^(n/2-1); fi; for d in divisors(n) do s := s+phi(d)*2^(n/d)/(2*n); od; RETURN(s); fi; end ...