A017668 Denominator of sum of -2nd powers of divisors of n.

1, 4, 9, 16, 25, 18, 49, 64, 81, 10, 121, 24, 169, 98, 45, 256, 289, 324, 361, 200, 441, 242, 529, 288, 625, 338, 729, 56, 841, 9, 961, 1024, 1089, 578, 49, 432, 1369, 722, 1521, 160, 1681, 441, 1849, 968, 2025, 1058, 2209, 1152, 2401, 500, 2601, 1352, 2809

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

Colin Defant, On the Density of Ranges of Generalized Divisor Functions, arXiv:1506.05432 [math.NT], 2015.

Formula

Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^2*(1 - x^k)). - Ilya Gutkovskiy, May 24 2018

Example

1, 5/4, 10/9, 21/16, 26/25, 25/18, 50/49, 85/64, 91/81, 13/10, 122/121, 35/24, 170/169, ...

Mathematica

Table[Denominator[DivisorSigma[-2, n]], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *)
Table[Denominator[DivisorSigma[2, n]/n^2], {n, 1, 50}] (* G. C. Greubel, Nov 08 2018 *)

Prog

(PARI) a(n) = denominator(sigma(n, -2)); \\ Michel Marcus, Aug 24 2018
(PARI) vector(50, n, denominator(sigma(n, 2)/n^2)) \\ G. C. Greubel, Nov 08 2018
(Magma) [Denominator(DivisorSigma(2, n)/n^2): n in [1..50]]; // G. C. Greubel, Nov 08 2018

Crossrefs

Cf. A017667 (numerator).

Sequence in context: A070448 A081403 A259602 * A225004 A339857 A074373

Adjacent sequences: A017665 A017666 A017667 * A017669 A017670 A017671

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved