A138761 a(n) is the smallest member of A000522 divisible by 2^n, where A000522(m) = total number of arrangements of a set with m elements.

1, 2, 16, 16, 16, 330665665962404000, 4216377920843140187197325631474390438452208808916276571342090223552

Offset: 0

Author

Jonathan Sondow, Apr 01 2008

Keywords

• nonn

Comments

a(n) < A000522(2^n) for n > 0; see Sondow and Schalm, Proposition A.13 part (ii).

Examples

			a(5) = A000522(19) = 330665665962404000 because that is the smallest member of A000522 divisible by 2^5.
		

References

• J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010.

Links

• Jean-François Alcover, Table of n, a(n) for n = 0..9
• J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II, arXiv:0709.0671 [math.NT], 2007-2009.
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000522, A127014, A127015.

Programs

Mathematica

a522[n_] := E Gamma[n + 1, 1];
(* b = A127014 *)
b[1] = 1; b[n_] := b[n] = For[k = b[n - 1], True, k++, If[Mod[a522[k], 2^n] == 0, Return[k]]];
a[0] = 1; a[n_] := a522[b[n]];
Table[a[n], {n, 0, 6}] (* Jean-François Alcover, Feb 20 2019 *)

Formula

a(n) = A000522(A127014(n)) = Sum_{k=0..A127014(n)} A127014(n)!/k! for n > 0.