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1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
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OFFSET
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1
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COMMENTS
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Conjectures:
1) The only distinct terms of this sequence are -1, 0 and 1.
2) The asymptotic density of the occurrences of 0 is 0.943..., and the asymptotic densities of the occurrences of -1 and 1 are equal and the common value is 0.028... .
These conjectures are empirically supported by the following numbers of occurrences of the terms -1, 0 and 1 up to n = 10^k:
k -1 0 1
- ------- ------- ------
1 0 6 4
2 1 87 12
3 28 913 59
4 362 9189 449
5 3159 93430 3411
6 27853 943571 28576
7 281802 9434309 283889
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LINKS
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FORMULA
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a(p) = 0 for an odd prime p.
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MATHEMATICA
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s[n_] := Length[Union[FactorInteger[n!][[;; , 2]]]]; s[1] = 0; Differences[Table[s[n], {n, 1, 100}]]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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