A017704 Denominator of sum of -20th powers of divisors of n.

1, 1048576, 3486784401, 1099511627776, 95367431640625, 1828079220031488, 79792266297612001, 1152921504606846976, 12157665459056928801, 50000000000000000000, 672749994932560009201, 638959998741245853696

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. A017703.

Programs

Magma

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

Mathematica

Denominator[DivisorSigma[-20,Range[20]]] (* Harvey P. Dale, Dec 31 2014 *)
Table[Denominator[DivisorSigma[20, n]/n^20], {n, 1, 20}] (* G. C. Greubel, Nov 05 2018 *)

PARI

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