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

1,3

Links

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

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

Prog

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

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.

Sequence in context: A236456 A046824 A130156 * A238444 A076742 A308284

Adjacent sequences: A139166 A139167 A139168 * A139170 A139171 A139172

Keyword

nonn

Author

Artur Jasinski, Apr 11 2008

Status

approved