

A017669


Numerator of sum of 3rd powers of divisors of n.


3



1, 9, 28, 73, 126, 7, 344, 585, 757, 567, 1332, 511, 2198, 387, 392, 4681, 4914, 757, 6860, 4599, 1376, 2997, 12168, 455, 15751, 9891, 20440, 3139, 24390, 147, 29792, 37449, 4144, 22113, 6192, 55261, 50654, 15435, 61544, 7371, 68922, 172, 79508, 24309, 10598
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OFFSET

1,2


COMMENTS

Sum_{dn} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665A017712 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), A001157A001160 (k=2,3,4,5), A013954A013972 for k = 6,7,...,24.  Ahmed Fares (ahmedfares(AT)mydeja.com), Apr 05 2001


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)


FORMULA

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


PROG

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


CROSSREFS

Cf. A017670.
Sequence in context: A062451 A065959 A226333 * A277065 A001158 A171215
Adjacent sequences: A017666 A017667 A017668 * A017670 A017671 A017672


KEYWORD

nonn,frac


AUTHOR

N. J. A. Sloane


STATUS

approved



