A101976 Number of products of factorials not exceeding n!.

1, 2, 4, 8, 15, 28, 49, 83, 134, 209, 317, 473, 687, 987, 1403, 1972, 2732, 3752, 5096, 6852, 9144, 12113, 15919, 20802, 27012, 34860, 44755, 57136, 72592, 91802, 115567, 144916, 180963

Offset: 1

Author

Jonathan Sondow, Dec 22 2004

Keywords

• nonn

Comments

a(n) is the position of n! in A001013 (Jordan-Polya numbers: products of factorials). a(n) > A101977(n) for n > 2 and a(n) > A101978(n) for n > 3.

Examples

			a(4) = 8 because 8 products of factorials do not exceed 4!, namely, 1, 2, 4, 6, 8, 12, 16 and 24.
		

Links

• Index entries for sequences related to factorial numbers.
• Eric Weisstein's World of Mathematics, Factorial Products

Crossrefs

Cf. A000142, A001013, A101977, A101978.

Programs

Mathematica

m[n_]:=(For[p=0; a=f=Table[k!, {k, 1, n}], p=!=a, p=a;a=Select[Union@@Outer[Times, f, a], #<=n!&]];a);Table[Length[m[n]], {n, 20}]

Extensions

a(21)-a(33) from Donovan Johnson, May 30 2012