A136032 Number of prime factors (with multiplicity) of Mersenne composites (A065341).

2, 2, 3, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 5, 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, 2, 5, 4, 5, 3, 5, 4

Offset: 1

Author

Artur Jasinski, Dec 11 2007

Keywords

• nonn

Comments

If the conjecture that all Mersenne composites are squarefree is true, then this sequence is identical to A135975. - Felix Fröhlich, Aug 24 2014

Links

• Amiram Eldar, Table of n, a(n) for n = 1..183

Crossrefs

Cf. A001222, A065341, A135975.

Programs

Mathematica

a = {}; Do[If[PrimeQ[n] && !PrimeQ[2^n - 1], w = 2^n - 1; c = FactorInteger[w]; d = Length[c]; b = 0; Do[b = b + c[[k]][[2]], {k, 1, d}]; AppendTo[a, b]], {n, 2, 150}]; a
PrimeOmega/@Select[2^Prime[Range[100]]-1,!PrimeQ[#]&] (* Harvey P. Dale, Nov 01 2016 *)

PARI

forprime(p=2, 1e3, if(!ispseudoprime(2^p-1), print1(bigomega(2^p-1), ", "))) \\ Felix Fröhlich, Aug 24 2014

Formula

a(n) = A001222(A065341(n)). - Michel Marcus, Aug 24 2014

Extensions

More terms from Michel Marcus, Nov 04 2013

Definition adjusted by Felix Fröhlich, Aug 24 2014

More terms from Felix Fröhlich, Aug 24 2014