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Search: id:A101976
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| A101976 |
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Number of products of factorials not exceeding n!. |
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+0
3
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| 1, 2, 4, 8, 15, 28, 49, 83, 134, 209, 317, 473, 687, 987, 1403, 1972, 2732, 3752, 5096, 6852
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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LINKS
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Index entries for sequences related to factorial numbers.
Eric Weisstein's World of Mathematics, Factorial Products
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EXAMPLE
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a(4) = 8 because 8 products of factorials do not exceed 4!, namely, 1, 2, 4, 6, 8, 12, 16, and 24.
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A000142, A001013, A101977, A101978.
Sequence in context: A138653 A054159 A056181 this_sequence A036615 A006808 A006727
Adjacent sequences: A101973 A101974 A101975 this_sequence A101977 A101978 A101979
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KEYWORD
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nonn
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 22 2004
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