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A017668 Denominator of sum of -2nd powers of divisors of n. 4
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 (list; graph; refs; listen; history; text; internal format)
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 A074373 A067115

Adjacent sequences:  A017665 A017666 A017667 * A017669 A017670 A017671

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 11 21:28 EST 2019. Contains 329937 sequences. (Running on oeis4.)