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A072298 Smallest integer k such that for no integer m, m! is divisible by n^k but not by n^(k+1). 1

%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 p-th 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

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Last modified April 18 14:39 EDT 2019. Contains 322209 sequences. (Running on oeis4.)