A017710 Denominator of sum of -23rd powers of divisors of n.

1, 8388608, 94143178827, 70368744177664, 11920928955078125, 65810851921133568, 27368747340080916343, 590295810358705651712, 8862938119652501095929, 50000000000000000000000, 895430243255237372246531

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. A017709.

Programs

Magma

[Denominator(DivisorSigma(23,n)/n^23): n in [1..20]]; // G. C. Greubel, Nov 03 2018

Mathematica

Table[Denominator[DivisorSigma[23, n]/n^23], {n, 1, 20}] (* G. C. Greubel, Nov 03 2018 *)

PARI

a(n) = denominator(sigma(n, 23)/n^23); \\ G. C. Greubel, Nov 03 2018