A017693 Numerator of sum of -15th powers of divisors of n.

1, 32769, 14348908, 1073774593, 30517578126, 13061093507, 4747561509944, 35185445863425, 205891146443557, 500015258805447, 4177248169415652, 3851873211923611, 51185893014090758, 19446605389919367, 48654880101420712, 1152956690052710401, 2862423051509815794

Offset

1,2

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

Formula

From Amiram Eldar, Apr 02 2024: (Start)

sup_{n>=1} a(n)/A017694(n) = zeta(15) (A013673).

Dirichlet g.f. of a(n)/A017694(n): zeta(s)*zeta(s+15).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A017694(k) = zeta(16) (A013674). (End)

Mathematica

Table[Numerator[DivisorSigma[15, n]/n^15], {n, 1, 20}] (* G. C. Greubel, Nov 06 2018 *)

Prog

(PARI) vector(20, n, numerator(sigma(n, 15)/n^15)) \\ G. C. Greubel, Nov 06 2018
(Magma) [Numerator(DivisorSigma(15, n)/n^15): n in [1..20]]; // G. C. Greubel, Nov 06 2018

Crossrefs

Cf. A017694 (denominator), A013673, A013674.

Sequence in context: A183817 A303267 A323545 * A013963 A036093 A217357

Adjacent sequences: A017690 A017691 A017692 * A017694 A017695 A017696

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved