A017694 Denominator of sum of -15th powers of divisors of n.

1, 32768, 14348907, 1073741824, 30517578125, 13060694016, 4747561509943, 35184372088832, 205891132094649, 500000000000000, 4177248169415651, 3851755393646592, 51185893014090757, 19446011944726528, 48654876708984375

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. A017693.

Programs

Magma

[Denominator(DivisorSigma(15,n)/n^15): n in [1..20]]; // G. C. Greubel, Nov 05 2018

Mathematica

Table[Denominator[DivisorSigma[15, n]/n^15], {n, 1, 20}] (* G. C. Greubel, Nov 05 2018 *)

PARI

vector(20, n, denominator(sigma(n, 15)/n^15)) \\ G. C. Greubel, Nov 05 2018