A017674 Denominator of sum of -5th powers of divisors of n.

1, 32, 243, 1024, 3125, 648, 16807, 32768, 59049, 50000, 161051, 62208, 371293, 67228, 253125, 1048576, 1419857, 629856, 2476099, 1600000, 4084101, 117128, 6436343, 663552, 9765625, 5940688, 14348907, 307328, 20511149, 337500, 28629151, 33554432, 13045131

Offset

1,2

Comments

Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^5*(1 - x^k)). - Ilya Gutkovskiy, May 25 2018

Example

1, 33/32, 244/243, 1057/1024, 3126/3125, 671/648, 16808/16807, 33825/32768, 59293/59049, ...

Mathematica

Table[Denominator[DivisorSigma[-5, n]], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
Table[Denominator[DivisorSigma[5, n]/n^5], {n, 1, 40}] (* G. C. Greubel, Nov 08 2018 *)

Prog

(PARI) vector(40, n, denominator(sigma(n, 5)/n^5)) \\ G. C. Greubel, Nov 08 2018
(Magma) [Denominator(DivisorSigma(5, n)/n^5): n in [1..40]]; // G. C. Greubel, Nov 08 2018

Crossrefs

Cf. A017673.

Sequence in context: A224136 A250363 A346637 * A184979 A257855 A055014

Adjacent sequences: A017671 A017672 A017673 * A017675 A017676 A017677

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved