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Number of distinct prime factors of p^p - 1 where p = prime(n).
2

%I #22 Jul 04 2024 03:29:37

%S 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

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

%F a(n) = A344870(A000040(n)). - _Amiram Eldar_, Jul 04 2024

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

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

%o (Python)

%o from sympy import factorint, prime

%o def a(n): p = prime(n); return len(factorint(p**p-1).values())

%o print([a(n) for n in range(1, 12)]) # _Michael S. Branicky_, May 27 2022

%Y Cf. A000040, A088730, A344870.

%K nonn,more

%O 1,2

%A _Cino Hilliard_, Nov 23 2003

%E More terms from _Ray Chandler_, Feb 21 2004

%E Name clarified, offset and data corrected and a(27)-a(33) added by _Amiram Eldar_, Jul 04 2024