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%I #27 Mar 05 2024 16:31:36
%S 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,
%T 9,9
%N Number of distinct prime factors of p^p + 1 where p is prime(n).
%C a(35) >= 9. See link to factordb.com - _Hugo Pfoertner_, Aug 07 2019
%H Chris Caldwell, <a href="https://t5k.org/lists/small/1000.txt">The First 1000 Primes</a>.
%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>
%H factordb.com, <a href="http://factordb.com/index.php?query=n%5En%2B1&use=n&n=100&VP=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=20&format=1&sent=Show">Status of prime(n)^prime(n)+1</a>.
%e If p=29 then (29^29 + 1) contains 7 distinct prime factors.
%t f[n_] := Length@ FactorInteger[Prime[n]^Prime[n] + 1]; Array[f, 20] (* _Robert G. Wilson v_, Apr 06 2006 *)
%o (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
%Y Cf. A125137.
%K nonn,more,hard
%O 1,2
%A _Parthasarathy Nambi_, Mar 14 2006
%E 8 more terms from _R. J. Mathar_, Mar 29 2006
%E a(19)-a(25) from _Robert G. Wilson v_, Apr 06 2006
%E a(26)-a(32) from _Sean A. Irvine_, Oct 20 2011
%E a(33)-a(34) from _Hugo Pfoertner_, Aug 07 2019
%E a(28) corrected by _Sean A. Irvine_, Aug 04 2023