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A017671 Numerator of sum of -4th powers of divisors of n. 3

%I #19 Sep 08 2022 08:44:43

%S 1,17,82,273,626,697,2402,4369,6643,5321,14642,3731,28562,20417,51332,

%T 69905,83522,112931,130322,85449,196964,124457,279842,179129,391251,

%U 242777,538084,46839,707282,218161,923522,1118481,1200644,41761,1503652,604513,1874162

%N Numerator of sum of -4th powers of divisors of n.

%C 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

%H G. C. Greubel, <a href="/A017671/b017671.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t Table[Numerator[DivisorSigma[-4, n]], {n, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 21 2011 *)

%t Table[Numerator[DivisorSigma[4, n]/n^4], {n, 1, 40}] (* _G. C. Greubel_, Nov 08 2018 *)

%o (PARI) vector(40, n, numerator(sigma(n, 4)/n^4)) \\ _G. C. Greubel_, Nov 08 2018

%o (Magma) [Numerator(DivisorSigma(4,n)/n^4): n in [1..40]]; // _G. C. Greubel_, Nov 08 2018

%Y Cf. A017672.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)