A017711 Numerator of sum of -24th powers of divisors of n.

1, 16777217, 282429536482, 281474993487873, 59604644775390626, 2369190810383965297, 191581231380566414402, 4722366764344638701569, 79766443077154939399843, 500000029802322396083921, 9849732675807611094711842, 13249475323675656646347131, 542800770374370512771595362

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..1000

Formula

Dirichlet g.f.: zeta(s)*zeta(s+24) (for fraction A017711/A017712). - Franklin T. Adams-Watters, Sep 11 2005

From Amiram Eldar, Apr 02 2024: (Start)

sup_{n>=1} a(n)/A017712(n) = zeta(24).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A017712(k) = zeta(25). (End)

Mathematica

Table[Numerator[DivisorSigma[24, n]/n^24], {n, 1, 20}] (* G. C. Greubel, Nov 03 2018 *)

Prog

(PARI) a(n) = numerator(sigma(n, 24)/n^24); \\ Michel Marcus, Nov 01 2013
(Magma) [Numerator(DivisorSigma(24, n)/n^24): n in [1..20]]; // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A017712 (denominator).

Sequence in context: A017328 A017448 A017580 * A013972 A036102 A230636

Adjacent sequences: A017708 A017709 A017710 * A017712 A017713 A017714

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved