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

1,2

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.

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A337257 A051487 A111286 * A309841 A132176 A197469

Adjacent sequences: A058292 A058293 A058294 * A058296 A058297 A058298

Keyword

nonn

Author

Leroy Quet, Dec 07 2000

Extensions

Corrected by Jonathan Sondow, Dec 18 2004

Status

approved