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A002744
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Sum of logarithmic numbers.
(Formerly M4682 N2001)
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5
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1, 0, 1, 10, -17, 406, -1437, 20476, -44907, 1068404, -5112483, 230851094, -1942311373, 31916614874, -27260241361, 3826126294680, -37957167335671, 2169009251237640, -25847377785179111, 858747698098918338, -5611513985867158697, 154094365406716365118
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listen;
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OFFSET
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1,4
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REFERENCES
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J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.
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) * log(Product_{k>=1} (1 - x^k)^(1/k)). - Ilya Gutkovskiy, Dec 11 2019
a(p) == -2 (mod p) for prime p. The pseudoprimes of this congruence are 4, 6, 20, 42, 1806, ... - Amiram Eldar, May 13 2020
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MATHEMATICA
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a[n_] := n! * Sum[(-1)^k * DivisorSigma[0, n - k]/k!/(n - k), {k, 0, n - 1}]; Array[a, 22] (* Amiram Eldar, May 13 2020 *)
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PROG
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(PARI) a(n) = sum(k=1, n, (-1)^(n-k)*numdiv(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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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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