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A165899
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Residue of n! after successive divisions by factors greater than n.
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1
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1, 2, 1, 4, 2, 1, 7, 2, 12, 5, 1, 18, 9, 1, 21, 9, 3, 1, 27, 10, 3, 1, 23, 6, 2, 25, 5, 3, 1, 18, 9, 2, 54, 18, 5, 1, 54, 19, 3, 1, 60, 18, 9, 2, 66, 23, 1, 3, 84, 7, 3, 1, 65, 18, 5, 1, 63, 21, 7, 1, 61, 45, 9, 2, 112, 27, 13, 3, 1, 54, 27, 6, 3, 1, 37, 12, 3, 1, 79, 20, 3, 1, 83, 27, 9, 1, 43
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OFFSET
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1,2
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LINKS
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EXAMPLE
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For n=8:
8!=40320 is divisible by 9 with a quotient of 4480;
4480 is divisible by 10 with a quotient of 448;
448 is not divisible by 11, 12 or 13, but is divisible by 14 with a quotient of 32;
32 is not divisible by 15, but is divisible by 16 with a quotient of 2;
2 is the final residue of the sequence since 16 > 2, therefore a(8)=2.
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MAPLE
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A165899 := proc(n) local f, d; f := n! ; d := n+1 ; while f >= d do if f mod d = 0 then f := f/d ; end if; d := d+1 ; end do ; f ; end proc: seq(A165899(n), n=1..80) ; # R. J. Mathar, Jan 25 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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