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Search: id:A101977
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| A101977 |
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Number of products of distinct factorials not exceeding n!. |
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+0
3
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| 1, 2, 3, 5, 7, 11, 15, 22, 31, 43, 58, 74, 97, 131, 171, 222, 277, 349, 447
(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 A058295 (products of distinct factorials). a(n) < A101976(n) for n > 2, and a(n) > A101978(n) for n > 10.
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LINKS
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Index entries for sequences related to factorial numbers.
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EXAMPLE
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a(4) = 5 because 5 products of distinct factorials do not exceed 4!, namely, 1, 2, 6, 12, and 24.
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A000142, A058295, A101976, A101978.
Sequence in context: A091955 A091584 A091582 this_sequence A024793 A116601 A024792
Adjacent sequences: A101974 A101975 A101976 this_sequence A101978 A101979 A101980
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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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