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A017673 Numerator of sum of -5th powers of divisors of n. 3
1, 33, 244, 1057, 3126, 671, 16808, 33825, 59293, 51579, 161052, 64477, 371294, 69333, 254248, 1082401, 1419858, 652223, 2476100, 1652091, 4101152, 120789, 6436344, 687775, 9768751, 6126351, 14408200, 317251, 20511150, 349591, 28629152, 34636833, 13098896 (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

Numerators 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[Numerator[DivisorSigma[-5, n]], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)

Table[Numerator[DivisorSigma[5, n]/n^5], {n, 1, 40}] (* G. C. Greubel, Nov 08 2018 *)

PROG

(PARI) vector(40, n, numerator(sigma(n, 5)/n^5)) \\ G. C. Greubel, Nov 08 2018

(MAGMA) [Numerator(DivisorSigma(5, n)/n^5): n in [1..40]]; // G. C. Greubel, Nov 08 2018

CROSSREFS

Cf. A017674.

Sequence in context: A088703 A321561 A034679 * A001160 A294300 A271208

Adjacent sequences:  A017670 A017671 A017672 * A017674 A017675 A017676

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)