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A013964 a(n) = sigma_16(n), the sum of the 16th powers of the divisors of n. 5
1, 65537, 43046722, 4295032833, 152587890626, 2821153019714, 33232930569602, 281479271743489, 1853020231898563, 10000152587956162, 45949729863572162, 184887084343023426, 665416609183179842, 2177986570740006274, 6568408508343827972 (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^16*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003

Dirichlet g.f.: zeta(s-16)*zeta(s). - Ilya Gutkovskiy, Sep 10 2016

MATHEMATICA

DivisorSigma[16, Range[30]] (* Vincenzo Librandi, Sep 10 2016 *)

PROG

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

(MAGMA) [DivisorSigma(16, n): n in [1..20]]; // Vincenzo Librandi, Sep 10 2016

(PARI) N=99; q='q+O('q^N); Vec(sum(n=1, N, n^16*q^n/(1-q^n))) \\ Altug Alkan, Sep 10 2016

CROSSREFS

Sequence in context: A070816 A133864 A017695 * A036094 A133865 A194185

Adjacent sequences:  A013961 A013962 A013963 * A013965 A013966 A013967

KEYWORD

nonn,mult,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 20 23:46 EDT 2021. Contains 343143 sequences. (Running on oeis4.)