A017697 Numerator of sum of -17th powers of divisors of n.

1, 131073, 129140164, 17180000257, 762939453126, 1410565726331, 232630513987208, 2251816993685505, 16677181828806733, 50000381469792099, 505447028499293772, 554657012677255537, 8650415919381337934, 3811447419980664273, 32842042032920650888, 295150156996346511361

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. A017698 (denominator), A013675, A013676.

Programs

Magma

[Numerator(DivisorSigma(17,n)/n^17): n in [1..20]]; // G. C. Greubel, Nov 05 2018

Mathematica

Table[Numerator[DivisorSigma[17, n]/n^17], {n, 1, 20}] (* G. C. Greubel, Nov 05 2018 *)

PARI

vector(20, n, numerator(sigma(n, 17)/n^17)) \\ G. C. Greubel, Nov 05 2018

Formula

From Amiram Eldar, Apr 02 2024: (Start)

sup_{n>=1} a(n)/A017698(n) = zeta(17) (A013675).

Dirichlet g.f. of a(n)/A017698(n): zeta(s)*zeta(s+17).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A017698(k) = zeta(18) (A013676). (End)