

A002746


Sum of logarithmic numbers.
(Formerly M3468 N1411)


7



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

1,2


REFERENCES

J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 7383.
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



FORMULA

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] * (k1)!, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Dec 16 2019 *)


PROG

(PARI) a(n) = sum(k=1, n, numdiv(k)*(k1)!*binomial(n, k)); \\ Michel Marcus, May 13 2020


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



