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

1,2

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.

Links

Table of n, a(n) for n=1..48.

Index entries for sequences related to factorial numbers.

Example

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

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}]

Crossrefs

Cf. A000142, A058295, A101976, A101978.

Sequence in context: A091582 A241727 A326465 * A024793 A326590 A116601

Adjacent sequences: A101974 A101975 A101976 * A101978 A101979 A101980

Keyword

nonn

Author

Jonathan Sondow, Dec 22 2004

Extensions

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

Status

approved