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

1,5

Comments

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A001348, A003260, A046051, A046932.

Sequence in context: A097886 A308293 A249298 * A053283 A035669 A126863

Adjacent sequences: A088860 A088861 A088862 * A088864 A088865 A088866

Keyword

nonn

Author

Jeppe Stig Nielsen, Nov 25 2003

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

Status

approved