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A013966 a(n) = sigma_18(n), the sum of the 18th powers of the divisors of n. 6
1, 262145, 387420490, 68719738881, 3814697265626, 101560344351050, 1628413597910450, 18014467229220865, 150094635684419611, 1000003814697527770, 5559917313492231482, 26623434909949071690 (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^18*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003

MATHEMATICA

Table[DivisorSigma[18, n], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)

PROG

(Sage) [sigma(n, 18)for n in range(1, 13)] # Zerinvary Lajos, Jun 04 2009

(PARI) a(n)=sigma(n, 18) \\ Charles R Greathouse IV, Apr 28 2011

(MAGMA) [DivisorSigma(18, n): n in [1..50]]; // G. C. Greubel, Nov 03 2018

CROSSREFS

Sequence in context: A017577 A051441 A017699 * A036096 A170792 A170801

Adjacent sequences:  A013963 A013964 A013965 * A013967 A013968 A013969

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.)