1,2

Or, a(n) = Sum_{ d divides n } n!/d. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 24 2005

Number of labeled regular octopi (or octopuses, cycles of ordered sets all the same size).

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 56 (1.4.67).

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 159, #10, A(n,1).

T. D. Noe, Table of n, a(n) for n=1..100

H. Ochiai, Counting functions for branched covers of elliptic curves and quasi-modular forms

a(p) = (p+1)*(p-1)! if p is a prime. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 24 2005

E.g.f.: log(f(x)), where f(x) = o.g.f. for partitions (A000041), Product_{k=1..inf} 1/(1-x^k) - N. J. A. Sloane (njas(AT)research.att.com).

E.g.f.: Sum_{k>0} x^k/(k*(1-x^k)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 27 2005

a(6) = 6!{1/1 +1/2 +1/3 + 1/6}=1440.

with(numtheory): a:=proc(n) local div: div:=divisors(n): n!*sum(1/div[j], j=1..tau(n)) end: seq(a(n), n=1..23); (Deutsch)

Left edge of triangle in A008298. Cf. A058892.

Cf. A057625.

Cf. A110373, A110374.

Sequence in context: A007175 A152394 A128322 this_sequence A051763 A074435 A039647

Adjacent sequences: A038045 A038046 A038047 this_sequence A038049 A038050 A038051

easy,nonn,nice

Christian G. Bower (bowerc(AT)usa.net)

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 24 2005

Edited by N. J. A. Sloane (njas(AT)research.att.com), May 12 2008 at the suggestion of Joerg Arndt.