A372599 Number of distinct prime factors of n^n-n.

1, 2, 3, 4, 4, 5, 4, 6, 5, 6, 5, 9, 5, 6, 12, 8, 4, 10, 5, 11, 7, 6, 7, 12, 8, 13, 8, 10, 6, 14, 8, 12, 9, 10, 18, 18, 6, 11, 11, 19, 8, 16, 5, 12, 13, 7, 7, 20, 5, 18, 12, 14, 7, 21, 12, 19, 10, 10, 7, 24, 7, 10, 20, 15, 13, 19, 6, 19, 11, 19, 9, 25, 6, 13

Offset: 2

Author

Tyler Busby, May 06 2024

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 2..115

Crossrefs

Cf. A001221, A061190, A372546, A372229, A344870, A344869.

Programs

Mathematica

a[n_] := a[n] = PrimeNu[n^n - n];
Table[a[n], {n, 2, 75}] (* Robert P. P. McKone, May 07 2024 *)

PARI

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

Python

from sympy.ntheory.factor_ import primenu
def A372599(n): return primenu(n*(n**(n-1)-1)) # Chai Wah Wu, May 07 2024

Formula

a(n) = A001221(A061190(n)).