%I #19 Jul 08 2023 10:41:47

%S 0,3,3,8,4,8,5,11,6,11,7,16,7,10,9,15,5,16,4,19,12,14,4,24,11,15,15,

%T 19,9,23,5,22,12,10,11,26,9,14,8,22,5,26,5,22,18,21,6,30,9,16,11,24,

%U 13,28,17,27,10,23,8,37,7,14,16,29,12,20,11,22,14,26,9,40

%N Number of prime factors of prime(n)^n-1, with multiplicity.

%H Amiram Eldar, <a href="/A069462/b069462.txt">Table of n, a(n) for n = 1..96</a> (using factordb.com)

%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=509%5E97-1">Status of 509^97-1</a>.

%F a(n) = A001222(A069459(n)).

%e A000040(8)^8-1 = 19^8-1 = 16983563040 = 2^5*3^2*5*17*181*3833, therefore a(8) = 11 and A069461(8) = 6.

%e A000040(9)^9-1 = 23^9-1 = 1801152661462 = 2*7*11*19*79*7792003, therefore a(9) = 6 and A069461(9) = 6.

%t Table[PrimeOmega[Prime[n]^n - 1], {n, 1, 30}] (* _Amiram Eldar_, Feb 17 2020 *)

%o (PARI) for(n=1,52,print1(bigomega(prime(n)^n-1)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

%Y Cf. A001222, A069459, A069461, A069465.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Mar 24 2002

%E More terms from _Hugo Pfoertner_, May 21 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

%E a(53)-a(72) using factordb.com from _Amiram Eldar_, Feb 17 2020