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A013970 a(n) = sum of 22nd powers of divisors of n. 5
1, 4194305, 31381059610, 17592190238721, 2384185791015626, 131621735227521050, 3909821048582988050, 73786993887028445185, 984770902214992292491, 10000002384185795209930, 81402749386839761113322 (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^22*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003

MATHEMATICA

lst={}; Do[AppendTo[lst, DivisorSigma[22, n]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)

a[ n_] := DivisorSigma[ 22, n]; (* Michael Somos, Dec 19 2016 *)

PROG

(Sage) [sigma(n, 22)for n in range(1, 12)] # Zerinvary Lajos, Jun 04 2009

(PARI) vector(50, n, sigma(n, 22)) \\ G. C. Greubel, Nov 03 2018

(MAGMA) [DivisorSigma(22, n): n in [1..50]]; // G. C. Greubel, Nov 03 2018

CROSSREFS

Sequence in context: A017447 A017579 A017707 * A036100 A236946 A258884

Adjacent sequences:  A013967 A013968 A013969 * A013971 A013972 A013973

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 21 01:53 EDT 2021. Contains 343143 sequences. (Running on oeis4.)