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A013972 a(n) = sigma_24(n), the sum of the 24th powers of the divisors of n. 79
1, 16777217, 282429536482, 281474993487873, 59604644775390626, 4738381620767930594, 191581231380566414402, 4722366764344638701569, 79766443077154939399843, 1000000059604644792167842, 9849732675807611094711842, 79496851942053939878082786, 542800770374370512771595362 (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
FORMULA
G.f.: Sum_{k>=1} k^24*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003
From Amiram Eldar, Oct 29 2023: (Start)
Multiplicative with a(p^e) = (p^(24*e+24)-1)/(p^24-1).
Dirichlet g.f.: zeta(s)*zeta(s-24).
Sum_{k=1..n} a(k) = zeta(25) * n^25 / 25 + O(n^26). (End)
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
KEYWORD
nonn,mult,easy
AUTHOR
STATUS
approved

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Last modified July 24 07:42 EDT 2024. Contains 374575 sequences. (Running on oeis4.)