A017690 Denominator of sum of -13th powers of divisors of n.

1, 8192, 1594323, 67108864, 1220703125, 1088391168, 96889010407, 549755813888, 2541865828329, 5000000000000, 34522712143931, 26748301344768, 302875106592253, 99214346656768, 648731689453125

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

Links

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

Crossrefs

Cf. A017689.

Programs

Magma

[Denominator(DivisorSigma(13,n)/n^13): n in [1..20]]; // G. C. Greubel, Nov 06 2018

Mathematica

Table[Denominator[DivisorSigma[13, n]/n^13], {n, 1, 20}] (* G. C. Greubel, Nov 06 2018 *)

PARI

vector(20, n, denominator(sigma(n, 13)/n^13)) \\ G. C. Greubel, Nov 06 2018