A017708 Denominator of sum of -22nd powers of divisors of n.

1, 4194304, 31381059609, 17592186044416, 2384185791015625, 65810851921133568, 3909821048582988049, 73786976294838206464, 984770902183611232881, 1000000000000000000000, 81402749386839761113321

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. A017707.

Programs

Magma

[Denominator(DivisorSigma(22,n)/n^22): n in [1..20]]; // G. C. Greubel, Nov 05 2018

Mathematica

Table[Denominator[DivisorSigma[22, n]/n^22], {n, 1, 20}] (* G. C. Greubel, Nov 05 2018 *)

PARI

vector(20, n, denominator(sigma(n, 22)/n^22)) \\ G. C. Greubel, Nov 05 2018