

A354226


a(n) is the number of distinct prime factors of (p^p  1)/(p  1) where p = prime(n).


0



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

1,3


COMMENTS

a(34) > 3, and depends on the full factorization of the 296digit composite number (139^139  1)/138.  Tyler Busby, Jan 22 2023
Sequence continues as ?, 8, ?, 5, 8, 4, 5, ?, 8, ?, 8, 7, 6, 3, 3, ..., where ? represents uncertain terms.  Tyler Busby, Jan 22 2023


LINKS



FORMULA



EXAMPLE

a(3)=2, since (5^5  1)/(5  1) = 11*71.


PROG

(PARI) a(n) = my(p=prime(n)); omega((p^p1)/(p1)); \\ Michel Marcus, May 22 2022
(Python)
from sympy import factorint, prime
def a(n): p = prime(n); return len(factorint((p**p1)//(p1)))


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



