A115973 Number of distinct prime factors of p^p + 1 where p is prime(n).

1, 2, 3, 3, 6, 5, 3, 5, 8, 7, 7, 7, 6, 8, 10, 8, 9, 8, 7, 8, 4, 7, 12, 6, 8, 7, 12, 11, 6, 9, 7, 17, 9, 9

Offset: 1

Author

Parthasarathy Nambi, Mar 14 2006

Keywords

• nonn
• more
• hard

Comments

a(35) >= 9. See link to factordb.com - Hugo Pfoertner, Aug 07 2019

Examples

			If p=29 then (29^29 + 1) contains 7 distinct prime factors.
		

Links

• Chris Caldwell, The First 1000 Primes.
• Dario Alejandro Alpern, Factorization using the Elliptic Curve Method
• factordb.com, Status of prime(n)^prime(n)+1.

Crossrefs

Cf. A125137.

Programs

Mathematica

f[n_] := Length@ FactorInteger[Prime[n]^Prime[n] + 1]; Array[f, 20] (* Robert G. Wilson v, Apr 06 2006 *)

PARI

{ for(n=1,20, p = prime(n); d = factor(p^p+1); dec=matsize(d); print1(dec[1],","); ); } \\ R. J. Mathar, Mar 29 2006

Extensions

8 more terms from R. J. Mathar, Mar 29 2006

a(19)-a(25) from Robert G. Wilson v, Apr 06 2006

a(26)-a(32) from Sean A. Irvine, Oct 20 2011

a(33)-a(34) from Hugo Pfoertner, Aug 07 2019

a(28) corrected by Sean A. Irvine, Aug 04 2023