A017712 Denominator of sum of -24th powers of divisors of n.

1, 16777216, 282429536481, 281474976710656, 59604644775390625, 2369190669160808448, 191581231380566414401, 4722366482869645213696, 79766443076872509863361, 500000000000000000000000, 9849732675807611094711841

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..1000

Crossrefs

Cf. A017711.

Programs

Magma

[Denominator(DivisorSigma(24,n)/n^24): n in [1..20]]; // G. C. Greubel, Nov 03 2018

Mathematica

Table[Denominator[DivisorSigma[24, n]/n^24], {n, 1, 20}] (* G. C. Greubel, Nov 03 2018 *)

PARI

a(n) = denominator(sigma(n, 24)/n^24); \\ Michel Marcus, Nov 01 2013