A017672 Denominator of sum of -4th powers of divisors of n.

1, 16, 81, 256, 625, 648, 2401, 4096, 6561, 5000, 14641, 3456, 28561, 19208, 50625, 65536, 83521, 104976, 130321, 80000, 194481, 117128, 279841, 165888, 390625, 228488, 531441, 43904, 707281, 202500, 923521, 1048576, 1185921, 39304, 1500625, 559872, 1874161

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

Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^4*(1 - x^k)). - Ilya Gutkovskiy, May 24 2018

Example

1, 17/16, 82/81, 273/256, 626/625, 697/648, 2402/2401, 4369/4096, 6643/6561, 5321/5000, ...

Mathematica

Table[Denominator[DivisorSigma[-4, n]], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *)
Table[Denominator[DivisorSigma[4, n]/n^4], {n, 1, 40}] (* G. C. Greubel, Nov 08 2018 *)

Prog

(PARI) vector(40, n, denominator(sigma(n, 4)/n^4)) \\ G. C. Greubel, Nov 08 2018
(Magma) [Denominator(DivisorSigma(4, n)/n^4): n in [1..40]]; // G. C. Greubel, Nov 08 2018

Crossrefs

Cf. A017671.

Sequence in context: A277562 A217709 A257854 * A055013 A080150 A000583

Adjacent sequences: A017669 A017670 A017671 * A017673 A017674 A017675

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved