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 A013972 Sum of 24th powers of divisors of n. 78

%I

%S 1,16777217,282429536482,281474993487873,59604644775390626,

%T 4738381620767930594,191581231380566414402,4722366764344638701569,

%U 79766443077154939399843,1000000059604644792167842,9849732675807611094711842

%N Sum of 24th powers of divisors of n.

%C If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).

%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. - comment from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001.

%F G.f.: sum(k>=1, k^24*x^k/(1-x^k)). - _Benoit Cloitre_, Apr 21 2003

%t lst={};Do[AppendTo[lst,DivisorSigma[24,n]],{n,5!}];lst [From _Vladimir Joseph Stephan Orlovsky_, Mar 11 2009]

%o (Sage) [sigma(n,24)for n in xrange(1,12)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2009]

%o (PARI) a(n)=sigma(n,24) \\ _Charles R Greathouse IV_, Apr 28, 2011

%K nonn,mult,easy,changed

%O 1,2

%A _N. J. A. Sloane_.

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