A354226 a(n) is the number of distinct prime factors of (p^p - 1)/(p - 1) where p = prime(n).

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

Offset

1,3

Comments

a(34) > 3, and depends on the full factorization of the 296-digit 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

Table of n, a(n) for n=1..33.

factordb, Status of (139^139 - 1)/138.

Formula

a(n) = A001221(A001039(n)).

Example

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

Prog

(PARI) a(n) = my(p=prime(n)); omega((p^p-1)/(p-1)); \\ Michel Marcus, May 22 2022
(Python)
from sympy import factorint, prime
def a(n): p = prime(n); return len(factorint((p**p-1)//(p-1)))
print([a(n) for n in range(1, 12)]) # Michael S. Branicky, May 23 2022

Crossrefs

Cf. A000040, A001039, A001221, A088790, A125135, A212552, A214812.

Sequence in context: A182663 A071452 A282495 * A341421 A308890 A081414

Adjacent sequences: A354223 A354224 A354225 * A354227 A354228 A354229

Keyword

nonn,more

Author

Luis H. Gallardo, May 20 2022

Extensions

a(18)-a(33) from Amiram Eldar, May 20 2022

Status

approved