A017680 Denominator of sum of -8th powers of divisors of n.

1, 256, 6561, 65536, 390625, 839808, 5764801, 16777216, 43046721, 50000000, 214358881, 71663616, 815730721, 737894528, 2562890625, 4294967296, 6975757441, 11019960576, 16983563041, 12800000000

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^8*(1 - x^k)). - Ilya Gutkovskiy, May 25 2018

Example

1, 257/256, 6562/6561, 65793/65536, 390626/390625, 843217/839808, 5764802/5764801, 16843009/16777216, ...

Mathematica

Table[Denominator[Total[1/Divisors[n]^8]], {n, 20}] (* Harvey P. Dale, Dec 16 2013 *)
Table[Denominator[DivisorSigma[8, n]/n^8], {n, 1, 20}] (* G. C. Greubel, Nov 07 2018 *)

Prog

(PARI) vector(20, n, denominator(sigma(n, 8)/n^8)) \\ G. C. Greubel, Nov 07 2018
(Magma) [Denominator(DivisorSigma(8, n)/n^8): n in [1..20]]; // G. C. Greubel, Nov 07 2018

Crossrefs

Cf. A017679.

Sequence in context: A321832 A351196 A016900 * A210840 A001016 A352054

Adjacent sequences: A017677 A017678 A017679 * A017681 A017682 A017683

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved