A165899 - OEIS

%I #7 Jan 13 2019 03:08:51

%S 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,

%T 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,

%U 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

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

%e For n=8:

%e 8!=40320 is divisible by 9 with a quotient of 4480;

%e 4480 is divisible by 10 with a quotient of 448;

%e 448 is not divisible by 11, 12 or 13, but is divisible by 14 with a quotient of 32;

%e 32 is not divisible by 15, but is divisible by 16 with a quotient of 2;

%e 2 is the final residue of the sequence since 16 > 2, therefore a(8)=2.

%p 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

%Y Cf. A000142.

%K nonn

%O 1,2

%A _Sergio Pimentel_, Sep 29 2009

%E Terms beyond a(15) from _R. J. Mathar_, Jan 25 2010