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A139169 a(n)=smallest k >= 1 such that n divides prime(k)!.

%I A139169 #12 Mar 08 2018 02:42:40
%S A139169 1,1,2,3,3,2,4,3,4,3,5,3,6,4,3,4,7,4,8,3,4,5,9,3,5,6,5,4,10,3,11,5,5,
%T A139169 7,4,4,12,8,6,3,13,4,14,5,4,9,15,4,7,5,7,6,16,5,5,4,8,10,17,3,18,11,4,
%U A139169 5,6,5,19,7,9,4,20,4,21,12,5,8,5,6,22,4,5,13,23,4,7,14,10,5,24,4,6,9,11,15
%N A139169 a(n)=smallest k >= 1 such that n divides prime(k)!.
%H A139169 Robert Israel, <a href="/A139169/b139169.txt">Table of n, a(n) for n = 1..10000</a>
%p A139169 f:= proc(n) local F,m,Q,E,p;
%p A139169   F:= ifactors(n)[2];
%p A139169   m:= nops(F);
%p A139169   Q:= map(t -> t[1],F);
%p A139169   E:= map(t -> t[2],F);
%p A139169   p:= max(Q)-1;
%p A139169   do
%p A139169     p:= nextprime(p);
%p A139169     if andmap(i -> add(floor(p/Q[i]^j),j=1..floor(log[Q[i]](p))) >= E[i], [$1..m]) then return p fi;
%p A139169   od
%p A139169 end proc:
%p A139169 f(1):= 2:
%p A139169 map(numtheory:-pi @ f, [$1..100]); # _Robert Israel_, Mar 07 2018
%t A139169 a = {}; Do[m = 1; While[ ! IntegerQ[Prime[m]!/n], m++ ]; AppendTo[a, m], {n, 1, 100}]; a
%o A139169 (PARI) a(n) = forprime(p=2,, if (!(p! % n), return (primepi(p)))); \\ _Michel Marcus_, Mar 08 2018
%Y A139169 Indices of primes in A139171.
%Y A139169 Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160-A139166, A139089, A139168-A139170.
%K A139169 nonn
%O A139169 1,3
%A A139169 _Artur Jasinski_, Apr 11 2008