A088863 Number of prime factors of n-th Mersenne number M(p_n).

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, 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, 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

Offset: 1

Author

Jeppe Stig Nielsen, Nov 25 2003

Keywords

• nonn

Examples

			a(5)=2 because M(p_5)=M(11)=2047 has 2 (not necessarily distinct) prime factors.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..197 (first 137 terms from Herman Jamke)
• Herman Jamke, The first 137 terms in detail

Crossrefs

Cf. A001348, A003260, A046051, A046932.

Programs

Maple

seq(nops(ifactor(2^ithprime(n)-1)),n=1..32); # Emeric Deutsch, Dec 23 2004

Mathematica

Do[m = 2^Prime[n] - 1; Print[Plus @@ Last /@ FactorInteger[m]], {n, 1, 50}] (* Ryan Propper, Jul 31 2005 *)

PARI

for(n=1,137,print1(bigomega(2^prime(n)-1)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007

Formula

a(n) = A001222(A001348(n)) = A001222(A000225(A000040(n))).

Extensions

14 more terms from Emeric Deutsch, Dec 23 2004

More terms from Ryan Propper, Jul 31 2005

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007