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A002745
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Sum of logarithmic numbers.
(Formerly M3909 N1604)
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7
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1, 5, 20, 96, 469, 3145, 20684, 173544, 1557105, 16215253, 159346604, 2230085528, 26985045333, 368730610729, 5628888393652, 97987283458928, 1475486672174337, 29097611462122437, 505383110562327268, 10970329921706735216
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listen;
history;
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OFFSET
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1,2
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REFERENCES
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J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.
Jeffrey Shallit, personal communication.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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E.g.f.: exp(x) * Sum_{k>=1} x^k / (k*(1 - x^k)). - Ilya Gutkovskiy, Dec 11 2019
a(p) == -1 (mod p) for prime p. The pseudoprimes of this congruence are 30, 858, 1722, ... - Amiram Eldar, May 13 2020
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MATHEMATICA
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Table[Sum[Binomial[n, k] * DivisorSigma[1, k] * (k-1)!, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Dec 16 2019 *)
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PROG
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(PARI) a(n) = sum(k=1, n, sigma(k)*(k-1)!*binomial(n, k)); \\ Michel Marcus, May 13 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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