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Denominator of sum of -11th powers of divisors of n.
3

%I #16 Sep 08 2022 08:44:43

%S 1,2048,177147,4194304,48828125,30233088,1977326743,8589934592,

%T 31381059609,50000000000,285311670611,185752092672,1792160394037,

%U 506195646208,2883251953125,17592186044416,34271896307633

%N Denominator of sum of -11th 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 Harvey P. Dale, <a href="/A017686/b017686.txt">Table of n, a(n) for n = 1..1000</a>

%t Denominator[DivisorSigma[-11,Range[20]]] (* _Harvey P. Dale_, Dec 18 2012 *)

%o (PARI) vector(20, n, denominator(sigma(n, 11)/n^11)) \\ _G. C. Greubel_, Nov 06 2018

%o (Magma) [Denominator(DivisorSigma(11,n)/n^11): n in [1..20]]; // _G. C. Greubel_, Nov 06 2018

%Y Cf. A017685.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_