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A006515 Mersenne numbers with at most 2 prime factors.

%I A006515 M2695 #31 Jul 08 2025 16:48:49
%S A006515 3,7,31,127,2047,8191,131071,524287,8388607,2147483647,137438953471,
%T A006515 2199023255551,576460752303423487,2305843009213693951,
%U A006515 147573952589676412927,9671406556917033397649407,618970019642690137449562111,158456325028528675187087900671
%N A006515 Mersenne numbers with at most 2 prime factors.
%D A006515 John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman and S. S. Wagstaff, Jr., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
%D A006515 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006515 Amiram Eldar, <a href="/A006515/b006515.txt">Table of n, a(n) for n = 1..53</a>
%H A006515 John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman and S. S. Wagstaff, Jr., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
%H A006515 C. K. Caldwell, <a href="http://www.utm.edu/research/primes/mersenne/index.html">Mersenne primes</a>.
%H A006515 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>.
%F A006515 a(n) = A000225(A006514(n)). - _Amiram Eldar_, Sep 19 2023
%p A006515 A006515 := proc(n) local i;
%p A006515 i := 2^(ithprime(n))-1:
%p A006515 if (nops(numtheory[factorset](i)) < 3) then
%p A006515    return i
%p A006515 fi: end: seq(A006515(n), n=1..19);
%t A006515 Select[Array[2^Prime[#] - 1 &, 25], PrimeOmega@ # <= 2 &] (* _Michael De Vlieger_, May 04 2017 *)
%Y A006515 Cf. A000225, A001348, A006514.
%K A006515 nonn
%O A006515 1,1
%A A006515 _N. J. A. Sloane_
%E A006515 More terms from _Sean A. Irvine_, May 04 2017