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A013958 sigma_10(n), the sum of the 10th powers of the divisors of n. 10
1, 1025, 59050, 1049601, 9765626, 60526250, 282475250, 1074791425, 3486843451, 10009766650, 25937424602, 61978939050, 137858491850, 289537131250, 576660215300, 1100586419201, 2015993900450 (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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for sequences related to sigma(n)

FORMULA

G.f. sum(k>=1, k^10*x^k/(1-x^k)). - Benoit Cloitre, Apr 21 2003

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^9)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 06 2017

MATHEMATICA

lst={}; Do[AppendTo[lst, DivisorSigma[10, n]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)

DivisorSigma[10, Range[20]] (* Harvey P. Dale, Jan 04 2012 *)

PROG

(Sage) [sigma(n, 10)for n in xrange(1, 18)] # Zerinvary Lajos, Jun 04 2009

(PARI) a(n)=sigma(n, 10) \\ Charles R Greathouse IV, Apr 28, 2011

(MAGMA) [DivisorSigma(10, n): n in [1..20]]; // Bruno Berselli, Apr 10 2013

CROSSREFS

Sequence in context: A031742 A321807 A017683 * A294305 A036088 A023002

Adjacent sequences:  A013955 A013956 A013957 * A013959 A013960 A013961

KEYWORD

nonn,mult,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 22 10:20 EDT 2019. Contains 328317 sequences. (Running on oeis4.)