A309941 Number of prime factors of n^n - 1, counted with multiplicity.

1, 2, 3, 4, 4, 4, 7, 8, 6, 4, 8, 6, 5, 7, 7, 7, 10, 4, 11, 10, 8, 6, 13, 13, 11, 9, 13, 10, 15, 4, 13, 12, 13, 10, 18, 11, 8, 10, 16, 9, 16, 6, 15, 18, 9, 5, 19, 20, 14, 15, 17, 8, 16, 12, 18, 10, 10, 5, 26, 8, 10, 14, 20, 19, 17, 9, 17, 12, 19, 7, 29, 15, 8, 11, 20, 13, 21, 8

Offset: 2

Author

Hugo Pfoertner, Aug 24 2019

Keywords

• nonn
• hard

Examples

			a(3) = 2: 3^3 - 1 = 26 = 2 * 13.
a(5) = 4: 5^5 - 1 = 3124 = 2^2 * 11 * 71.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..138 (terms 2..126 from Chai Wah Wu)
• factordb, Factors of n^n-1.

Crossrefs

Cf. A006486, A048861, A085723, A116895, A125135, A334167, A344870.

Programs

Mathematica

a[n_] := PrimeOmega[n^n - 1]; Array[a, 45, 2] (* Amiram Eldar, Jul 04 2024 *)

PARI

for(k=2, 50, print1(bigomega(k^k-1),", "))