A378157 The least prime dividing !n = A000166(n).

2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 11, 2, 3, 2, 23, 2, 5, 2, 3, 2, 29, 2, 31, 2, 3, 2, 5, 2, 11, 2, 3, 2, 11, 2, 43, 2, 3, 2, 47, 2, 7, 2, 3, 2, 53, 2, 5, 2, 3, 2, 11, 2, 61, 2, 3, 2, 5, 2, 67, 2, 3, 2, 71, 2, 73, 2, 3, 2, 7, 2, 79, 2, 3, 2

Offset: 3

Author

Amiram Eldar, Nov 18 2024

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A000166, A020639, A152024, A195207, A195208, A195209, A195210, A378158, A378159.

Programs

Mathematica

lpf[n_] := Module[{p = 2}, While[! Divisible[n, p], p = NextPrime[p]]; p]; Array[lpf[Subfactorial[#]] &, 50, 3]

PARI

lpf(n) = {my(p = 2); while(n % p, p = nextprime(p+1)); p;}
lista(nmax) = {my(s = 1); for(n = 3, nmax, s = n * s + (-1)^n; print1(lpf(s), ", ")); }

Formula

a(n) = A020639(A000166(n)).

a(n) = min(A020639(n-1), A378159(n-2)) for n >= 2.