cp's OEIS Frontend

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

%I A115973 #27 Mar 05 2024 16:31:36
%S A115973 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 A115973 9,9
%N A115973 Number of distinct prime factors of p^p + 1 where p is prime(n).
%C A115973 a(35) >= 9. See link to factordb.com - _Hugo Pfoertner_, Aug 07 2019
%H A115973 Chris Caldwell, <a href="https://t5k.org/lists/small/1000.txt">The First 1000 Primes</a>.
%H A115973 Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>
%H A115973 factordb.com, <a href="http://factordb.com/index.php?query=n%5En%2B1&amp;use=n&amp;n=100&amp;VP=on&amp;OD=on&amp;PR=on&amp;FF=on&amp;PRP=on&amp;CF=on&amp;U=on&amp;C=on&amp;perpage=20&amp;format=1&amp;sent=Show">Status of prime(n)^prime(n)+1</a>.
%e A115973 If p=29 then (29^29 + 1) contains 7 distinct prime factors.
%t A115973 f[n_] := Length@ FactorInteger[Prime[n]^Prime[n] + 1]; Array[f, 20] (* _Robert G. Wilson v_, Apr 06 2006 *)
%o A115973 (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 A115973 Cf. A125137.
%K A115973 nonn,more,hard
%O A115973 1,2
%A A115973 _Parthasarathy Nambi_, Mar 14 2006
%E A115973 8 more terms from _R. J. Mathar_, Mar 29 2006
%E A115973 a(19)-a(25) from _Robert G. Wilson v_, Apr 06 2006
%E A115973 a(26)-a(32) from _Sean A. Irvine_, Oct 20 2011
%E A115973 a(33)-a(34) from _Hugo Pfoertner_, Aug 07 2019
%E A115973 a(28) corrected by _Sean A. Irvine_, Aug 04 2023