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 A013956 sigma_8(n), the sum of the 8th powers of the divisors of n. 12
 1, 257, 6562, 65793, 390626, 1686434, 5764802, 16843009, 43053283, 100390882, 214358882, 431733666, 815730722, 1481554114, 2563287812, 4311810305, 6975757442, 11064693731, 16983563042, 25700456418 (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 FORMULA G.f. Sum_{k>=1} k^8*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003 L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^7)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 06 2017 MATHEMATICA Table[DivisorSigma[8, n], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *) PROG (Sage) [sigma(n, 8)for n in range(1, 21)] # Zerinvary Lajos, Jun 04 2009 (PARI) a(n)=sigma(n, 8) \\ Charles R Greathouse IV, Apr 28, 2011 (MAGMA) [DivisorSigma(8, n): n in [1..30]]; // Bruno Berselli, Apr 10 2013 CROSSREFS Sequence in context: A321564 A034682 A017679 * A294303 A036086 A000542 Adjacent sequences:  A013953 A013954 A013955 * A013957 A013958 A013959 KEYWORD nonn,mult,easy AUTHOR STATUS approved

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Last modified February 19 13:03 EST 2020. Contains 332044 sequences. (Running on oeis4.)