A058295 Products of distinct factorials.

1, 2, 6, 12, 24, 48, 120, 144, 240, 288, 720, 1440, 2880, 4320, 5040, 5760, 8640, 10080, 17280, 30240, 34560, 40320, 60480, 80640, 86400, 103680, 120960, 172800, 207360, 241920, 362880, 483840, 518400, 604800, 725760, 967680, 1036800, 1209600

Offset: 1

Author

Leroy Quet, Dec 07 2000

Keywords

• nonn

Comments

(A075082(n)!)^2 is a member for n>0, for example, (6!)^2=6!*5!*3!. Factorials A000142 and superfactorials A000178 (without their first terms), double-superfactorials A098694 and product-of-next-n-factorials A074319 are all subsequences. Products-of-factorials A001013 is a supersequence. - Jonathan Sondow, Dec 18 2004

A000197(n)^2 is a member for n > 2, as ((n!)!)^2 = (n!)!*n!*(n!-1)!. - Jonathan Sondow, Dec 21 2004

Erdős & Graham show that there are exp((1+o(1))n log log n / log n) members of this sequence using no factorials above n.

Examples

			288 is included because 288 = 2! * 3! * 4!.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Paul Erdős and Ron L. Graham, On products of factorials, Bull. Inst. Math. Acad. Sinica 4:2 (1976), pp. 337-355.
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A075082, A000142, A000178, A098694, A074319, A001013, A000197.

Programs

Mathematica

k=10; m=1; With[{p=With[{s=Subsets[Table[n!, {n, 2, k}]]}, Sort[Table[Apply[Times, s[[n]]], {n, Length[s]}]]]}, While[p[[m]]<(k+1)!, m++ ]; Union[Take[p, m-1]]] (* Jonathan Sondow *)

PARI

list(lim)=my(v=List([1]),n=1,t=1);while((t=n++!)<=lim,for(i=1,#v,if(v[i]*t<=lim,listput(v,v[i]*t))));vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Mar 26 2012

Extensions

Corrected by Jonathan Sondow, Dec 18 2004