A165899 Residue of n! after successive divisions by factors greater than n.

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

Offset

1,2

Links

Table of n, a(n) for n=1..87.

Example

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.

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) ; # R. J. Mathar, Jan 25 2010

Crossrefs

Cf. A000142.

Sequence in context: A059370 A084534 A345877 * A316354 A104582 A209439

Adjacent sequences: A165896 A165897 A165898 * A165900 A165901 A165902

Keyword

nonn

Author

Sergio Pimentel, Sep 29 2009

Extensions

Terms beyond a(15) from R. J. Mathar, Jan 25 2010

Status

approved