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A017671 Numerator of sum of -4th powers of divisors of n. 3
1, 17, 82, 273, 626, 697, 2402, 4369, 6643, 5321, 14642, 3731, 28562, 20417, 51332, 69905, 83522, 112931, 130322, 85449, 196964, 124457, 279842, 179129, 391251, 242777, 538084, 46839, 707282, 218161, 923522, 1118481, 1200644, 41761, 1503652, 604513, 1874162 (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

FORMULA

Numerators of coefficients in expansion of Sum_{k>=1} x^k/(k^4*(1 - x^k)). - Ilya Gutkovskiy, May 24 2018

EXAMPLE

1, 17/16, 82/81, 273/256, 626/625, 697/648, 2402/2401, 4369/4096, 6643/6561, 5321/5000, ...

MATHEMATICA

Table[Numerator[DivisorSigma[-4, n]], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *)

Table[Numerator[DivisorSigma[4, n]/n^4], {n, 1, 40}] (* G. C. Greubel, Nov 08 2018 *)

PROG

(PARI) vector(40, n, numerator(sigma(n, 4)/n^4)) \\ G. C. Greubel, Nov 08 2018

(MAGMA) [Numerator(DivisorSigma(4, n)/n^4): n in [1..40]]; // G. C. Greubel, Nov 08 2018

CROSSREFS

Cf. A017672.

Sequence in context: A321560 A034678 A065960 * A001159 A053820 A294288

Adjacent sequences:  A017668 A017669 A017670 * A017672 A017673 A017674

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 11 18:50 EST 2019. Contains 329031 sequences. (Running on oeis4.)