A139171 a(n) = smallest prime number p such that p!/n is an integer.
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, 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, 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
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
- Wikipedia, Legendre's formula
Crossrefs
Programs
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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(f, [$1..100]); # Robert Israel, Mar 07 2018 -
Mathematica
a = {}; Do[m = 1; While[ ! IntegerQ[Prime[m]!/n], m++ ]; AppendTo[a, Prime[m]], {n, 1, 100}]; a -
PARI
a(n) = forprime(p=2,, if (!(p! % n), return (p))); \\ Michel Marcus, Mar 08 2018