A017678 - OEIS

%I #22 Sep 08 2022 08:44:43

%S 1,128,2187,16384,78125,23328,823543,2097152,4782969,5000000,19487171,

%T 8957952,62748517,13176688,56953125,268435456,410338673,204073344,

%U 893871739,640000000,1801088541,623589472

%N Denominator of sum of -7th 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 Vincenzo Librandi, <a href="/A017678/b017678.txt">Table of n, a(n) for n = 1..1000</a>

%F Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^7*(1 - x^k)). - _Ilya Gutkovskiy_, May 25 2018

%e 1, 129/128, 2188/2187, 16513/16384, 78126/78125, 23521/23328, 823544/823543, 2113665/2097152, ...

%t Table[Denominator[Total[Divisors[n]^-7]],{n,30}] (* _Harvey P. Dale_, Mar 21 2012 *)

%t Table[Denominator[DivisorSigma[7, n]/n^7], {n, 1, 20}] (* _G. C. Greubel_, Nov 07 2018 *)

%o (PARI) vector(20, n, denominator(sigma(n, 7)/n^7)) \\ _G. C. Greubel_, Nov 07 2018

%o (Magma) [Denominator(DivisorSigma(7,n)/n^7): n in [1..20]]; // _G. C. Greubel_, Nov 07 2018

%Y Cf. A017677.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_