The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A264859 a(n) is the denominator of c(n), where c(n) is calculated from Product_{i>=1}(1-c(i)*x^i) = exp(-(x^2)/(1-x))*(1-x). 1
1, 1, 1, 2, 1, 6, 1, 8, 3, 10, 1, 36, 1, 14, 15, 128, 1, 648, 1, 800, 21, 22, 1, 13824, 5, 26, 81, 6272, 1, 972000, 1, 32768, 33, 34, 35, 3359232, 1, 38, 39, 20480000, 1, 96018048, 1, 247808, 30375, 46, 1, 4586471424, 7, 500000, 51, 1384448, 1, 204073344, 55 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
c(1) = 1 and for n>1, c(n) satisfies Sum_{d|n} (1/d)*c(n/d)^d = 1 + 1/n.
c(p) = 1 for prime p and a(p) = 1 accordingly.
LINKS
MAPLE
c := proc (n) option remember; 1+1/n-add(procname(n/d)^d/d, d = `minus`(numtheory:-divisors(n), {1})) end proc: c(1) := 1: a := denom(map(c, [`$`(1 .. 100)]));
MATHEMATICA
nmax = 100; Remove[c]; Subscript[c, 1] = 1; Do[Subscript[c, k] = Subscript[c, k] /. (Flatten[Solve[SeriesCoefficient[E^(-x^2/(1 - x))*(1 - x), {x, 0, k}] == Coefficient[Expand[Product[1 - Subscript[c, i]*x^i, {i, 1, k}]], x^k], Subscript[c, k]]]), {k, 2, nmax}]; Table[Subscript[c, n], {n, 1, nmax}] // Denominator (* Vaclav Kotesovec, Dec 12 2015 *)
PROG
(PARI) lista(nn) = {vc = vector(nn); vc[1] = 1; for (n=2, nn, vc[n] = 1+1/n - sumdiv(n, d, if (d==1, 0, (vc[n/d]^d)/d)); print1(denominator(vc[n]), ", "); ); } \\ Michel Marcus, Nov 27 2015
CROSSREFS
Cf. A259027 (numerators).
Sequence in context: A324370 A324193 A364829 * A007956 A107754 A181569
KEYWORD
nonn,frac
AUTHOR
Gevorg Hmayakyan, Nov 26 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 23 10:34 EDT 2024. Contains 372760 sequences. (Running on oeis4.)