A101977 Number of products of distinct factorials not exceeding n!.

1, 2, 3, 5, 7, 11, 15, 22, 31, 43, 58, 74, 97, 131, 171, 222, 277, 349, 447, 564, 698, 868, 1074, 1321, 1601, 1967, 2398, 2911, 3513, 4235, 5083, 6071, 7242, 8637, 10229, 12102, 14293, 16848, 19802, 23271, 27276, 31846, 37132, 43196, 50191, 58238, 67425, 77946

Offset: 1

Author

Jonathan Sondow, Dec 22 2004

Keywords

• nonn

Comments

a(n) is the position of n! in A058295 (products of distinct factorials). a(n) < A101976(n) for n > 2 and a(n) > A101978(n) for n > 10.

Examples

			a(4) = 5 because 5 products of distinct factorials do not exceed 4!, namely, 1, 2, 6, 12 and 24.
		

Links

• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A000142, A058295, A101976, A101978.

Programs

Mathematica

d[k_] := (m=1; With[{p=With[{s=Subsets[Table[n!, {n, k}]]}, Sort[Table[Apply[Times, s[[n]]], {n, Length[s]}]]]}, While[p[[m]]<=k!, m++ ]; Length[Union[Take[p, m-1]]]]);Table[d[k], {k, 19}]

Extensions

a(20)-a(48) from Donovan Johnson, May 30 2012