A088807 Number of distinct prime factors of p^p - 1 where p = prime(n).

1, 2, 3, 4, 4, 5, 4, 3, 6, 9, 4, 9, 7, 6, 5, 7, 5, 7, 9, 7, 12, 8, 6, 8, 8, 11, 8, 6, 7, 10, 9, 7, 13

Offset: 1

Author

Cino Hilliard, Nov 23 2003

Keywords

• nonn
• more

Crossrefs

Cf. A000040, A088730, A344870.

Programs

Mathematica

PrimeNu/@Table[p^p-1,{p,Prime[Range[30]]}] (* The program takes a long time to run. *) (* Harvey P. Dale, Sep 05 2020 *)

PARI

omegaptop(n,m) = { sr=0; forprime(x=2,n, y=omega(x^x-m); print1(y","); sr += 1.0/y; ); print(); }

Python

from sympy import factorint, prime
def a(n): p = prime(n); return len(factorint(p**p-1).values())
print([a(n) for n in range(1, 12)]) # Michael S. Branicky, May 27 2022

Formula

a(n) = A344870(A000040(n)). - Amiram Eldar, Jul 04 2024

Extensions

More terms from Ray Chandler, Feb 21 2004

Name clarified, offset and data corrected and a(27)-a(33) added by Amiram Eldar, Jul 04 2024