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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| Example: For n=8, a(8)=2 because: 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
| 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) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 25 2010]
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CROSSREFS
| A000142
Sequence in context: A035607 A059370 A084534 * A104582 A133938 A074586
Adjacent sequences: A165896 A165897 A165898 * A165900 A165901 A165902
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KEYWORD
| nonn
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AUTHOR
| Sergio Pimentel (ferdiego(AT)suddenlink.com), Sep 29 2009
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EXTENSIONS
| Terms beyond a(15) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 25 2010
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