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 A002746 Sum of logarithmic numbers. (Formerly M3468 N1411) 5
 1, 4, 13, 50, 203, 1154, 6627, 49356, 403293, 3858376, 33929377, 460614670, 5168544119, 64518640406, 946910125319, 16124114481720, 221243980745433, 4261440137319852, 68524390012831189, 1477309421907315082 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES 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). LINKS 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. FORMULA 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 MATHEMATICA Table[Sum[Binomial[n, k] * DivisorSigma[0, k] * (k-1)!, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Dec 16 2019 *) PROG (PARI) a(n) = sum(k=1, n, numdiv(k)*(k-1)!*binomial(n, k)); \\ Michel Marcus, May 13 2020 CROSSREFS Cf. A000005, A002744, A318249. Sequence in context: A149456 A149457 A149458 * A149459 A149460 A219579 Adjacent sequences:  A002743 A002744 A002745 * A002747 A002748 A002749 KEYWORD nonn AUTHOR EXTENSIONS Corrected and extended by Jeffrey Shallit. More terms from Vladeta Jovovic, Feb 09 2003 STATUS approved

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Last modified May 27 13:56 EDT 2022. Contains 354097 sequences. (Running on oeis4.)