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A101977
Number of products of distinct factorials not exceeding n!.
2
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.
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
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Dec 22 2004
EXTENSIONS
a(20)-a(48) from Donovan Johnson, May 30 2012
STATUS
approved