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 A082245 Sum of (n-1)-th powers of divisors of n. 8
 1, 3, 10, 73, 626, 8052, 117650, 2113665, 43053283, 1001953638, 25937424602, 743375541244, 23298085122482, 793811662272744, 29192932133689220, 1152956690052710401, 48661191875666868482, 2185928253847184914509 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = t(n,n-1), t as defined in A082771; a(1)=A000005(1), a(2)=A000203(2), a(3)=A001157(3), a(4)=A001158(4), a(5)=A001159(5), a(6)=A001160(6), a(7)=A013954(7), a(8)=A013955(8). LINKS Seiichi Manyama, Table of n, a(n) for n = 1..387 M. Sugunamma, Certain results concerning sigma_k(n) and phi_k(n), Annales Polonici Mathematici, Vol. 8, No. 2 (1960), pp. 173-176. Eric Weisstein's World of Mathematics, Divisor Function. FORMULA G.f.: Sum_{k>=1} k^(k-1)*x^k/(1 - (k*x)^k). - Ilya Gutkovskiy, Nov 02 2018 L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)^(1/k^2)) = Sum_{k>=1} a(k)*x^k/k. - Seiichi Manyama, Jun 23 2019 Limit_{n->oo} a(n)/A023887(n-1) = e (A001113) (Sugunamma, 1960). - Amiram Eldar, Apr 15 2021 EXAMPLE a(6) = 1^5 + 2^5 + 3^5 + 6^5 = 1 + 32 + 243 + 7776 = 8052. MATHEMATICA Table[Total[Divisors[n]^(n-1)], {n, 18}] (* T. D. Noe, Oct 25 2006 *) Table[DivisorSigma[n-1, n], {n, 1, 20}] (* G. C. Greubel, Nov 02 2018 *) PROG (Sage) [sigma(n, (n-1))for n in range(1, 19)] # Zerinvary Lajos, Jun 04 2009 (PARI) a(n) = sigma(n, n-1); \\ Michel Marcus, Nov 07 2017 (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k*x)^k)^(1/k^2))))) \\ Seiichi Manyama, Jun 23 2019 (Magma) [DivisorSigma(n-1, n): n in [1..20]]; // G. C. Greubel, Nov 02 2018 CROSSREFS Cf. A023887, A000005, A000203, A001157, A001158, A001159, A001160, A013954, A013955, A013956, A013957, A013958 Cf. A013959, A013960, A013961, A013962, A013963, A013964, A013965, A013966, A013967, A013968, A013969, A013970 Cf. A001113, A013971, A013972. Sequence in context: A337949 A086846 A277614 * A158033 A027159 A236696 Adjacent sequences: A082242 A082243 A082244 * A082246 A082247 A082248 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 22 2003 EXTENSIONS Corrected by T. D. Noe, Oct 25 2006 STATUS approved

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Last modified February 29 14:32 EST 2024. Contains 370425 sequences. (Running on oeis4.)