A344870 Number of distinct prime factors of n^n-1.

1, 2, 3, 3, 4, 4, 6, 6, 5, 4, 8, 5, 5, 7, 7, 4, 8, 3, 11, 9, 8, 6, 12, 11, 8, 9, 11, 9, 14, 4, 12, 8, 13, 10, 18, 9, 8, 10, 15, 7, 16, 6, 14, 17, 8, 5, 18, 17, 13, 14, 17, 7, 15, 10, 18, 8, 10, 5, 26, 7, 9, 14, 19, 14, 17, 9, 15, 11, 19, 7, 29, 12, 7, 11, 19, 12, 21, 8, 22, 25, 6, 6, 26, 16, 9, 15, 21, 8, 26, 11, 15, 13, 11, 11, 25, 8, 12, 14, 26

Offset: 2

Author

Seiichi Manyama, May 31 2021

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 2..138
• factordb, Factors of n^n-1.

Crossrefs

Cf. A001221, A048861, A309941, A334167, A344869.

Programs

Magma

[#PrimeDivisors(n^n-1): n in [2..100]];

Mathematica

a[n_] := PrimeNu[n^n - 1]; Array[a, 45, 2] (* Amiram Eldar, Jun 01 2021 *)

PARI

a(n) = omega(n^n-1);

Formula

a(n) = A001221(A048861(n)).