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A013963 a(n) = sigma_15(n), the sum of the 15th powers of the divisors of n. 10
1, 32769, 14348908, 1073774593, 30517578126, 470199366252, 4747561509944, 35185445863425, 205891146443557, 1000030517610894, 4177248169415652, 15407492847694444, 51185893014090758, 155572843119354936, 437893920912786408, 1152956690052710401 (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^15*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003

Dirichlet g.f.: zeta(s-15)*zeta(s). - Ilya Gutkovskiy, Sep 10 2016

MATHEMATICA

DivisorSigma[15, Range[30]] (* Vincenzo Librandi, Sep 10 2016 *)

PROG

(Sage) [sigma(n, 15)for n in range(1, 15)] # Zerinvary Lajos, Jun 04 2009

(MAGMA) [DivisorSigma(15, n): n in [1..20]]; // Vincenzo Librandi, Sep 10 2016

(PARI) N=99; q='q+O('q^N); Vec(sum(n=1, N, n^15*q^n/(1-q^n))) \\ Altug Alkan, Sep 10 2016

CROSSREFS

Sequence in context: A303267 A323545 A017693 * A036093 A217357 A083603

Adjacent sequences:  A013960 A013961 A013962 * A013964 A013965 A013966

KEYWORD

nonn,mult,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 21 23:52 EDT 2021. Contains 343156 sequences. (Running on oeis4.)