A017682 Denominator of sum of -9th powers of divisors of n.

1, 512, 19683, 262144, 1953125, 93312, 40353607, 134217728, 387420489, 500000000, 2357947691, 1289945088, 10604499373, 2582630848, 1423828125, 68719476736, 118587876497, 7346640384, 322687697779

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• frac

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

Examples

			1, 513/512, 19684/19683, 262657/262144, 1953126/1953125, 93499/93312, 40353608/40353607, 134480385/134217728, ...
		

Links

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

Crossrefs

Cf. A017681.

Programs

Magma

[Denominator(DivisorSigma(9,n)/n^9): n in [1..20]]; // G. C. Greubel, Nov 07 2018

Mathematica

Table[Denominator[DivisorSigma[9, n]/n^9], {n, 1, 20}] (* G. C. Greubel, Nov 07 2018 *)

PARI

vector(20, n, denominator(sigma(n, 9)/n^9)) \\ G. C. Greubel, Nov 07 2018

Formula

Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^9*(1 - x^k)). - Ilya Gutkovskiy, May 25 2018