A017684 Denominator of sum of -10th powers of divisors of n.

1, 1024, 59049, 1048576, 9765625, 30233088, 282475249, 1073741824, 3486784401, 200000000, 25937424601, 10319560704, 137858491849, 144627327488, 23066015625, 1099511627776, 2015993900449, 3570467226624

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, 1025/1024, 59050/59049, 1049601/1048576, 9765626/9765625, 30263125/30233088, 282475250/282475249, ...
		

Links

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

Crossrefs

Cf. A017683.

Programs

Magma

[Denominator(DivisorSigma(10,n)/n^10): n in [1..20]]; // G. C. Greubel, Nov 06 2018

Mathematica

Table[Denominator[DivisorSigma[10, n]/n^10], {n, 1, 20}] (* G. C. Greubel, Nov 06 2018 *)

PARI

vector(20, n, denominator(sigma(n, 10)/n^10)) \\ G. C. Greubel, Nov 06 2018

Formula

Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^10*(1 - x^k)). - Ilya Gutkovskiy, May 25 2018