A135976 - OEIS

%I #20 May 23 2021 02:51:12

%S 2047,8388607,137438953471,2199023255551,576460752303423487,

%T 147573952589676412927,9671406556917033397649407,

%U 158456325028528675187087900671,2535301200456458802993406410751

%N Mersenne composites (A065341) with exactly 2 prime factors.

%H Amiram Eldar, <a href="/A135976/b135976.txt">Table of n, a(n) for n = 1..39</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Semiprime">Semiprime</a>.

%F a(n) = 2^A135978(n) - 1. - _Amiram Eldar_, May 23 2021

%p A135976 := proc(n) local i;

%p i := 2^(ithprime(n))-1:

%p if (nops(numtheory[factorset](i)) = 2) then

%p    RETURN (i)

%p fi: end: [ seq(A135976(n), n=1..26) ]; # _Jani Melik_, Feb 09 2011

%t 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

%o (PARI) forprime(p=1, 1e2, if(bigomega(2^p-1)==2, print1(2^p-1, ", "))) \\ _Felix Fröhlich_, Aug 12 2014

%Y Subsequence of A065341.

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

%K nonn

%O 1,1

%A _Artur Jasinski_, Dec 09 2007