A017692 Denominator of sum of -14th powers of divisors of n.

1, 16384, 4782969, 268435456, 6103515625, 39182082048, 678223072849, 4398046511104, 22876792454961, 10000000000000, 379749833583241, 213986410758144, 3937376385699289, 5556003412779008, 5838585205078125

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. A017691.

Programs

Magma

[Denominator(DivisorSigma(14,n)/n^14): n in [1..20]]; // G. C. Greubel, Nov 06 2018

Mathematica

Table[Denominator[DivisorSigma[14, n]/n^14], {n, 1, 20}] (* G. C. Greubel, Nov 06 2018 *)

PARI

vector(20, n, denominator(sigma(n, 14)/n^14)) \\ G. C. Greubel, Nov 06 2018