A366580 Number of distinct prime divisors of 3^n + 1.

1, 1, 2, 2, 2, 2, 3, 2, 3, 4, 3, 3, 3, 2, 4, 5, 2, 4, 4, 3, 3, 5, 4, 2, 6, 4, 4, 6, 4, 4, 5, 3, 2, 6, 4, 4, 4, 4, 4, 7, 5, 3, 7, 2, 5, 9, 4, 4, 4, 4, 6, 8, 4, 3, 5, 6, 6, 7, 4, 3, 7, 3, 5, 11, 2, 4, 6, 3, 5, 8, 8, 6, 8, 3, 5, 11, 6, 5, 7, 4, 5, 11, 5, 5, 10, 8

Offset: 0

Author

Sean A. Irvine, Oct 13 2023

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 0..691

Crossrefs

Cf. A001221, A002592, A034472, A046799, A057935, A057941, A074476, A133801, A274909, A366577, A366578, A366579.

Programs

Mathematica

PrimeNu[3^Range[0,100]+1] (* Paolo Xausa, Oct 14 2023 *)

PARI

for(n = 0, 100, print1(omega(3^n + 1), ", "))

Formula

a(n) = omega(3^n+1) = A001221(A034472(n)).