login
Number of distinct prime factors of prime(n)^n+1.
2

%I #21 Jul 08 2023 17:38:30

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

%T 8,11,11,6,6,10,8,9,9,4,7,16,4,7,10,9,6,14,7,4,11,13,9,11,9,3,8,9,7,

%U 18,6,17,14,5,7,12,14,8,15,6,13,18,8,18,14,5,10,15,9

%N Number of distinct prime factors of prime(n)^n+1.

%H Dario Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method.</a>

%H FactorDB, <a href="http://factordb.com/index.php?query=431%5E83%2B1">Status of 431^83+1</a>.

%F a(n) = A001221(A062006(n)).

%e A000040(10)^10+1 = 29^10+1 = 420707233300202 = 2*421*1061*470925821, therefore a(10) = 4 and A069465(10) = 4.

%t Table[PrimeNu[Prime[n]^n + 1], {n, 1, 50}] (* _G. C. Greubel_, May 08 2017 *)

%o (PARI) a(n) = omega(prime(n)^n+1); \\ _Michel Marcus_, Feb 17 2020

%Y Cf. A001221, A062006, A069461, A069465.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Mar 24 2002

%E More terms from _Hugo Pfoertner_, May 21 2004

%E a(36) corrected and a(46)-a(82) added using factordb.com by _Amiram Eldar_, Feb 17 2020