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A013971 a(n) = sum of 23rd powers of divisors of n. 6
1, 8388609, 94143178828, 70368752566273, 11920928955078126, 789730317205170252, 27368747340080916344, 590295880727458217985, 8862938119746644274757, 100000011920928963466734, 895430243255237372246532 (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

Harvey P. Dale and Seiichi Manyama, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Index entries for sequences related to sigma(n)

FORMULA

G.f.: Sum_{k>=1} k^23*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003

MATHEMATICA

DivisorSigma[23, Range[15]] (* Harvey P. Dale, May 02 2016 *)

PROG

(Sage) [sigma(n, 23)for n in range(1, 12)] # Zerinvary Lajos, Jun 04 2009

(PARI) vector(30, n, sigma(n, 23)) \\ G. C. Greubel, Nov 03 2018

(MAGMA) [DivisorSigma(23, n): n in [1..30]]; // G. C. Greubel, Nov 03 2018

CROSSREFS

Sequence in context: A010811 A323660 A017709 * A036101 A283031 A160673

Adjacent sequences:  A013968 A013969 A013970 * A013972 A013973 A013974

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 21 02:10 EDT 2021. Contains 343143 sequences. (Running on oeis4.)