%I
%S 2,3,6,5,3,7,4,12,5,11,7,13,7,5,62,17,12,19,5,7,11,23,4,30,13,39,7,29,
%T 5,31,37,11,17,7,12,37,19,13,5,41,7,43,11,23,23,47,62,56,30,17,13,53,
%U 39,11,7,19,29,59,5,61,31,7,84,13,11,67,17,23,7,71,12,73,37,30,19,11
%N Smallest integer k such that for no integer m, m! is divisible by n^k but not by n^(k+1).
%C If p is a prime, the pth term is p.
%H Ivan Neretin, <a href="/A072298/b072298.txt">Table of n, a(n) for n = 2..2000</a>
%p for b from 2 do if isprime(b) then print(b): next: end if: L := ifactors(b)[2]: last := 0: for n from 2 to 10000 do C := [seq(0,i=1..nops(L))]: for i from 1 while 2^i <= n do for j from 1 to nops(L) do C := subsop(j=C[j]+floor(n/(L[j][1])^i), C): end do: end do: for j from 1 to nops(L) do C := subsop(j=floor(C[j]/(L[j][2])), C): end do: new := min(op(C)): if last + 1 < new then print(last+1): break: end if: last := new: end do: end do:
%K nonn
%O 2,1
%A _Asger Grunnet_, Jul 13 2002
