A017676 Denominator of sum of -6th powers of divisors of n.

1, 64, 729, 4096, 15625, 23328, 117649, 262144, 531441, 100000, 1771561, 497664, 4826809, 3764768, 2278125, 16777216, 24137569, 34012224, 47045881, 32000000, 85766121, 56689952, 148035889, 95551488, 244140625, 11881376, 387420489, 240945152, 594823321

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^6*(1 - x^k)). - Ilya Gutkovskiy, May 25 2018

Example

1, 65/64, 730/729, 4161/4096, 15626/15625, 23725/23328, 117650/117649, 266305/262144, ...

Mathematica

A017676[n_Integer] := Denominator[DivisorSigma[-6, n]]; A017676 /@ Range[100] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
Table[Denominator[DivisorSigma[6, n]/n^6], {n, 1, 20}] (* G. C. Greubel, Nov 07 2018 *)

Prog

(PARI) vector(20, n, denominator(sigma(n, 6)/n^6)) \\ G. C. Greubel, Nov 07 2018
(Magma) [Denominator(DivisorSigma(6, n)/n^6): n in [1..20]]; // G. C. Greubel, Nov 07 2018

Crossrefs

Cf. A017675.

Sequence in context: A016899 A250364 A346638 * A055015 A001014 A352052

Adjacent sequences: A017673 A017674 A017675 * A017677 A017678 A017679

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved