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

1,2

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.

Links

Table of n, a(n) for n=1..33.

Index entries for sequences related to factorial numbers.

Eric Weisstein's World of Mathematics, Factorial Products

Example

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

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}]

Crossrefs

Cf. A000142, A001013, A101977, A101978.

Sequence in context: A222028 A338760 A056181 * A339656 A196723 A036615

Adjacent sequences: A101973 A101974 A101975 * A101977 A101978 A101979

Keyword

nonn

Author

Jonathan Sondow, Dec 22 2004

Extensions

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

Status

approved