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A013962 a(n) = sigma_14(n), the sum of the 14th powers of the divisors of n. 6
1, 16385, 4782970, 268451841, 6103515626, 78368963450, 678223072850, 4398314962945, 22876797237931, 100006103532010, 379749833583242, 1283997101947770, 3937376385699290, 11112685048647250, 29192932133689220, 72061992352890881, 168377826559400930 (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^14*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003

Dirichlet g.f.: zeta(s-14)*zeta(s). - Ilya Gutkovskiy, Sep 10 2016

MATHEMATICA

DivisorSigma[14, Range[20]] (* Harvey P. Dale, Mar 10 2013 *)

PROG

(Sage) [sigma(n, 14)for n in range(1, 16)] # Zerinvary Lajos, Jun 04 2009

(MAGMA) DivisorSigma(14, n): n in [1..20]]; // Vincenzo Librandi, Sep 10 2016

(PARI) N=99; q='q+O('q^N); Vec(sum(n=1, N, n^14*q^n/(1-q^n))) \\ Altug Alkan, Sep 10 2016

CROSSREFS

Sequence in context: A160868 A230635 A017691 * A036092 A282597 A031673

Adjacent sequences:  A013959 A013960 A013961 * A013963 A013964 A013965

KEYWORD

nonn,mult,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 20 01:20 EDT 2021. Contains 343117 sequences. (Running on oeis4.)