A002746 Sum of logarithmic numbers. (Formerly M3468 N1411)

1, 4, 13, 50, 203, 1154, 6627, 49356, 403293, 3858376, 33929377, 460614670, 5168544119, 64518640406, 946910125319, 16124114481720, 221243980745433, 4261440137319852, 68524390012831189, 1477309421907315082

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.

Index entries for sequences related to logarithmic numbers

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: A149457 A149458 A364742 * A149459 A149460 A219579

Adjacent sequences: A002743 A002744 A002745 * A002747 A002748 A002749

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Corrected and extended by Jeffrey Shallit

More terms from Vladeta Jovovic, Feb 09 2003

Status

approved