A139171 - OEIS

%I #15 Mar 08 2018 03:01:43

%S 2,2,3,5,5,3,7,5,7,5,11,5,13,7,5,7,17,7,19,5,7,11,23,5,11,13,11,7,29,

%T 5,31,11,11,17,7,7,37,19,13,5,41,7,43,11,7,23,47,7,17,11,17,13,53,11,

%U 11,7,19,29,59,5,61,31,7,11,13,11,67,17,23,7,71,7,73,37,11,19,11,13,79,7,11

%N a(n) = smallest prime number p such that p!/n is an integer.

%H Robert Israel, <a href="/A139171/b139171.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre%27s_formula">Legendre's formula</a>

%p f:= proc(n) local F,m,Q,E,p;

%p   F:= ifactors(n)[2];

%p   m:= nops(F);

%p   Q:= map(t -> t[1],F);

%p   E:= map(t -> t[2],F);

%p   p:= max(Q)-1;

%p   do

%p     p:= nextprime(p);

%p     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   od

%p end proc:

%p f(1):= 2:

%p map(f, [$1..100]); # _Robert Israel_, Mar 07 2018

%t a = {}; Do[m = 1; While[ ! IntegerQ[Prime[m]!/n], m++ ]; AppendTo[a, Prime[m]], {n, 1, 100}]; a

%o (PARI) a(n) = forprime(p=2,, if (!(p! % n), return (p))); \\ _Michel Marcus_, Mar 08 2018

%Y Prime equivalent of Kempner numbers A002034.

%Y For quotients p!/n see A139170.

%Y For indices of primes in this sequence see A139169.

%Y Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160-A139166, A139089, A139168-A139170.

%K nonn,look

%O 1,1

%A _Artur Jasinski_, Apr 11 2008