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A017674 Denominator of sum of -5th powers of divisors of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A223952 A224136 A250363 * A184979 A257855 A055014

Adjacent sequences:  A017671 A017672 A017673 * A017675 A017676 A017677

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 16 08:18 EDT 2021. Contains 347469 sequences. (Running on oeis4.)