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A013972 a(n) = sum of 24th powers of divisors of n. 79
1, 16777217, 282429536482, 281474993487873, 59604644775390626, 4738381620767930594, 191581231380566414402, 4722366764344638701569, 79766443077154939399843, 1000000059604644792167842, 9849732675807611094711842 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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).

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

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sigma(n)

FORMULA

G.f.: Sum_{k>=1} k^24*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003

MATHEMATICA

Table[DivisorSigma[24, n], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)

PROG

(Sage) [sigma(n, 24)for n in range(1, 12)] # Zerinvary Lajos, Jun 04 2009

(PARI) a(n)=sigma(n, 24) \\ Charles R Greathouse IV, Apr 28, 2011

(Magma) [DivisorSigma(24, n): n in [1..50]]; // G. C. Greubel, Nov 03 2018

CROSSREFS

Sequence in context: A017448 A017580 A017711 * A036102 A230636 A283029

Adjacent sequences: A013969 A013970 A013971 * A013973 A013974 A013975

KEYWORD

nonn,mult,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 2 17:25 EST 2022. Contains 358510 sequences. (Running on oeis4.)