A069464 Number of distinct prime factors of prime(n)^n+1.

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

Offset: 1

Author

Reinhard Zumkeller, Mar 24 2002

Keywords

• nonn

Examples

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

Links

• Dario Alpern, Factorization using the Elliptic Curve Method.
• FactorDB, Status of 431^83+1.

Crossrefs

Cf. A001221, A062006, A069461, A069465.

Programs

Mathematica

Table[PrimeNu[Prime[n]^n + 1], {n, 1, 50}] (* G. C. Greubel, May 08 2017 *)

PARI

a(n) = omega(prime(n)^n+1); \\ Michel Marcus, Feb 17 2020

Formula

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

Extensions

More terms from Hugo Pfoertner, May 21 2004

a(36) corrected and a(46)-a(82) added using factordb.com by Amiram Eldar, Feb 17 2020