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A002746
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Sum of logarithmic numbers.
(Formerly M3468 N1411)
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5
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1, 4, 13, 50, 203, 1154, 6627, 49356, 403293, 3858376, 33929377, 460614670, 5168544119, 64518640406, 946910125319, 16124114481720, 221243980745433, 4261440137319852, 68524390012831189, 1477309421907315082
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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.
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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Amiram Eldar, Table of n, a(n) for n = 1..450
J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. [Annotated scanned copy]
J. M. Gandhi, Logarithmic Numbers and the Functions d(n) and sigma(n), The American Mathematical Monthly, Vol. 73, No. 9 (1966), pp. 959-964, alternative link.
Index entries for sequences related to logarithmic numbers
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FORMULA
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a(n) = Sum_{k=1..n} A000005(k)*(k-1)!*binomial(n, k). - Vladeta Jovovic, Feb 09 2003
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, 12, 30, 380, 858, 1722 ... - Amiram Eldar, May 13 2020
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MATHEMATICA
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Table[Sum[Binomial[n, k] * DivisorSigma[0, 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, numdiv(k)*(k-1)!*binomial(n, k)); \\ Michel Marcus, May 13 2020
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CROSSREFS
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Cf. A000005, A002744, A318249.
Sequence in context: A149456 A149457 A149458 * A149459 A149460 A219579
Adjacent sequences: A002743 A002744 A002745 * A002747 A002748 A002749
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Corrected and extended by Jeffrey Shallit.
More terms from Vladeta Jovovic, Feb 09 2003
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STATUS
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approved
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