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A017689 Numerator of sum of -13th powers of divisors of n. 3
1, 8193, 1594324, 67117057, 1220703126, 1088524711, 96889010408, 549822930945, 2541867422653, 5000610355659, 34522712143932, 26751583696117, 302875106592254, 99226457784093, 648732096885608 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

G. C. Greubel, Table of n, a(n) for n = 1..10000

MAPLE

A017689 := proc(n)

    numtheory[sigma][-13](n) ;

    numer(%) ;

end proc: # R. J. Mathar, Sep 21 2017

MATHEMATICA

Table[Numerator[DivisorSigma[13, n]/n^13], {n, 1, 20}] (* G. C. Greubel, Nov 06 2018 *)

PROG

(PARI) vector(20, n, numerator(sigma(n, 13)/n^13)) \\ G. C. Greubel, Nov 06 2018

(MAGMA) [Numerator(DivisorSigma(13, n)/n^13): n in [1..20]]; // G. C. Greubel, Nov 06 2018

CROSSREFS

Cf. A017690.

Sequence in context: A035908 A323544 A230190 * A013961 A036091 A181134

Adjacent sequences:  A017686 A017687 A017688 * A017690 A017691 A017692

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 22 04:02 EDT 2019. Contains 323473 sequences. (Running on oeis4.)