A366660 Number of distinct prime divisors of 9^n - 1.

1, 2, 3, 3, 3, 5, 3, 5, 6, 5, 5, 7, 3, 6, 8, 6, 6, 9, 5, 7, 8, 8, 4, 12, 7, 6, 11, 9, 7, 12, 6, 7, 10, 9, 8, 12, 6, 8, 12, 11, 6, 14, 4, 12, 16, 7, 8, 15, 10, 12, 13, 9, 6, 15, 11, 14, 13, 10, 5, 18, 5, 10, 16, 8, 9, 15, 6, 13, 13, 15, 7, 19, 7, 10, 19, 13, 11

Offset: 1

Author

Sean A. Irvine, Oct 15 2023

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..690

Crossrefs

Cf. A024101, A001221, A057952, A366661, A366662, A366663.

Cf. A046800, A133801, A366604, A366611, A366620, A366632, A366651, A102347, A366681, A366707.

Programs

PARI

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

Formula

a(n) = omega(9^n-1) = A001221(A024101(n)).

a(n) = A133801(2*n) = A133801(n) + A366580(n) - 1. - Max Alekseyev, Jan 07 2024