A135976 Mersenne composites (A065341) with exactly 2 prime factors.

2047, 8388607, 137438953471, 2199023255551, 576460752303423487, 147573952589676412927, 9671406556917033397649407, 158456325028528675187087900671, 2535301200456458802993406410751

Offset: 1

Author

Artur Jasinski, Dec 09 2007

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..39
• Wikipedia, Semiprime.

Crossrefs

Subsequence of A065341.

Cf. A000225, A054723, A134852, A135975, A135977, A135978, A135979.

Programs

Maple

A135976 := proc(n) local i;
i := 2^(ithprime(n))-1:
if (nops(numtheory[factorset](i)) = 2) then
   RETURN (i)
fi: end: [ seq(A135976(n), n=1..26) ]; # Jani Melik, Feb 09 2011

Mathematica

k = {}; Do[If[ ! PrimeQ[2^Prime[n] - 1], c = FactorInteger[2^Prime[n] - 1]; d = Length[c]; If[d == 2, AppendTo[k, 2^Prime[n] - 1]]], {n, 1, 40}]; k

PARI

forprime(p=1, 1e2, if(bigomega(2^p-1)==2, print1(2^p-1, ", "))) \\ Felix Fröhlich, Aug 12 2014

Formula

a(n) = 2^A135978(n) - 1. - Amiram Eldar, May 23 2021