A002745 Sum of logarithmic numbers. (Formerly M3909 N1604)

1, 5, 20, 96, 469, 3145, 20684, 173544, 1557105, 16215253, 159346604, 2230085528, 26985045333, 368730610729, 5628888393652, 97987283458928, 1475486672174337, 29097611462122437, 505383110562327268, 10970329921706735216

Offset

1,2

References

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).

Links

Amiram Eldar, Table of n, a(n) for n = 1..449

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} A000203(k)*(k-1)!*binomial(n, k). - Vladeta Jovovic, Feb 09 2003

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

Mathematica

Table[Sum[Binomial[n, k] * DivisorSigma[1, k] * (k-1)!, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Dec 16 2019 *)

Prog

(PARI) a(n) = sum(k=1, n, sigma(k)*(k-1)!*binomial(n, k)); \\ Michel Marcus, May 13 2020

Crossrefs

Cf. A000203, A002743.

Sequence in context: A352149 A196532 A377152 * A182959 A224661 A357786

Adjacent sequences: A002742 A002743 A002744 * A002746 A002747 A002748

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Feb 09 2003

Status

approved