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%I #19 May 13 2022 11:20:40
%S 1,1,1,1,2,1,1,1,2,3,1,2,2,3,3,3,2,1,2,3,3,3,2,1,2,2,2,1,2,5,1,2,2,2,
%T 2,5,4,5,2,4,3,4,5,3,2,2,3,6,2,4,4,6,2,5,3,4,2,2,3,2,3,2,5,3,4,4,3,5,
%U 2,3,3,6,5,2,2,5,3,9,4,3,5,2,8,4,4,3,5,2,4,6,3,4,2,7,3,4,4,1,2,5,4,5,3,5,4
%N Number of prime factors of n-th Mersenne number M(p_n).
%C a(n) = A001222(A001348(n)) = A001222(A000225(A000040(n)).
%H Max Alekseyev, <a href="/A088863/b088863.txt">Table of n, a(n) for n = 1..197</a> (first 137 terms from Herman Jamke)
%H Herman Jamke, <a href="/A088863/a088863.txt">The first 137 terms in detail</a>
%e a(5)=2 because M(p_5)=M(11)=2047 has 2 (not necessarily distinct) prime factors.
%p seq(nops(ifactor(2^ithprime(n)-1)),n=1..32); # _Emeric Deutsch_, Dec 23 2004
%t Do[m = 2^Prime[n] - 1; Print[Plus @@ Last /@ FactorInteger[m]], {n, 1, 50}] (* _Ryan Propper_, Jul 31 2005 *)
%o (PARI) for(n=1,137,print1(bigomega(2^prime(n)-1)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007
%Y Cf. A001348, A003260, A046051, A046932.
%K nonn
%O 1,5
%A _Jeppe Stig Nielsen_, Nov 25 2003
%E 14 more terms from _Emeric Deutsch_, Dec 23 2004
%E More terms from _Ryan Propper_, Jul 31 2005
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007
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