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

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, 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, 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

Offset: 1

Author

Artur Jasinski, Apr 11 2008

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Indices of primes in A139171.

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

Programs

Maple

f:= proc(n) local F,m,Q,E,p;
  F:= ifactors(n)[2];
  m:= nops(F);
  Q:= map(t -> t[1],F);
  E:= map(t -> t[2],F);
  p:= max(Q)-1;
  do
    p:= nextprime(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;
  od
end proc:
f(1):= 2:
map(numtheory:-pi @ f, [$1..100]); # Robert Israel, Mar 07 2018

Mathematica

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

PARI

a(n) = forprime(p=2,, if (!(p! % n), return (primepi(p)))); \\ Michel Marcus, Mar 08 2018