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A017667 Numerator of sum of -2 th powers of divisors of n. 2
1, 5, 10, 21, 26, 25, 50, 85, 91, 13, 122, 35, 170, 125, 52, 341, 290, 455, 362, 273, 500, 305, 530, 425, 651, 425, 820, 75, 842, 13, 962, 1365, 1220, 725, 52, 637, 1370, 905, 1700, 221, 1682, 625, 1850, 1281, 2366, 1325, 2210, 1705, 2451, 651, 2900, 1785 (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. - comment from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001.

LINKS

Table of n, a(n) for n=1..52.

FORMULA

Dirichlet generating function: zeta(s)*zeta(s+2) [for fraction A017667/A017668]. - Franklin T. Adams-Watters, Sep 11 2005.

MATHEMATICA

A017667[n_Integer] := Numerator[DivisorSigma[-2, n]]; A017667 /@ Range[100] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *)

CROSSREFS

Cf. A017668.

Sequence in context: A106367 A002791 A080399 * A001157 A002800 A132174

Adjacent sequences:  A017664 A017665 A017666 * A017668 A017669 A017670

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 23 13:33 EDT 2014. Contains 240928 sequences.