A017702 Denominator of sum of -19th powers of divisors of n.

1, 524288, 1162261467, 274877906944, 19073486328125, 50779978334208, 11398895185373143, 144115188075855872, 1350851717672992089, 5000000000000000000, 61159090448414546291, 79869999842655731712

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. A017701.

Programs

Magma

[Denominator(DivisorSigma(19,n)/n^19): n in [1..20]]; // G. C. Greubel, Nov 05 2018

Mathematica

Table[Denominator[DivisorSigma[19, n]/n^19], {n, 1, 20}] (* G. C. Greubel, Nov 05 2018 *)

PARI

vector(20, n, denominator(sigma(n, 19)/n^19)) \\ G. C. Greubel, Nov 05 2018