A017670 Denominator of sum of -3rd powers of divisors of n.

1, 8, 27, 64, 125, 6, 343, 512, 729, 500, 1331, 432, 2197, 343, 375, 4096, 4913, 648, 6859, 4000, 1323, 2662, 12167, 384, 15625, 8788, 19683, 2744, 24389, 125, 29791, 32768, 3993, 19652, 6125, 46656, 50653, 13718, 59319, 6400, 68921, 147, 79507, 21296, 10125

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

Denominator of Sum_{d|n} 1/d^3.

Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^3*(1 - x^k)). - Ilya Gutkovskiy, May 24 2018

Example

1, 9/8, 28/27, 73/64, 126/125, 7/6, 344/343, 585/512, 757/729, 567/500, 1332/1331, 511/432, ...

Mathematica

Table[Denominator[DivisorSigma[-3, n]], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *)
Table[Denominator[DivisorSigma[3, n]/n^3], {n, 1, 40}] (* G. C. Greubel, Nov 08 2018 *)

Prog

(PARI) vector(40, n, denominator(sigma(n, 3)/n^3)) \\ G. C. Greubel, Nov 08 2018
(Magma) [Denominator(DivisorSigma(3, n)/n^3): n in [1..40]]; // G. C. Greubel, Nov 08 2018

Crossrefs

Cf. A017669.

Sequence in context: A211641 A062686 A093322 * A353621 A126200 A213491

Adjacent sequences: A017667 A017668 A017669 * A017671 A017672 A017673

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved