A366664 Number of distinct prime divisors of 9^n + 1.

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

Offset: 0

Author

Sean A. Irvine, Oct 15 2023

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 0..345

Crossrefs

Cf. A062396, A001221, A057935, A366660, A366665, A366666, A366667.

Cf. A046799, A366580, A366605, A366615, A366627, A366636, A366655, A119704, A366686, A366712.

Programs

Mathematica

PrimeNu[9^Range[0,90]+1] (* Harvey P. Dale, Jul 04 2024 *)

PARI

for(n = 0, 100, print1(omega(9^n + 1), ", "))

Formula

a(n) = omega(9^n+1) = A001221(A062396(n)).

a(n) = A366580(2*n). - Max Alekseyev, Jan 08 2024