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Mersenne numbers with at most 2 prime factors.
(Formerly M2695)
1

%I M2695 #27 Sep 19 2023 01:44:18

%S 3,7,31,127,2047,8191,131071,524287,8388607,2147483647,137438953471,

%T 2199023255551,576460752303423487,2305843009213693951,

%U 147573952589676412927,9671406556917033397649407,618970019642690137449562111,158456325028528675187087900671

%N Mersenne numbers with at most 2 prime factors.

%D 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 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Amiram Eldar, <a href="/A006515/b006515.txt">Table of n, a(n) for n = 1..53</a>

%H 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 C. K. Caldwell, <a href="http://www.utm.edu/research/primes/mersenne/index.html">Mersenne primes</a>.

%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>.

%F a(n) = A000225(A006514(n)). - _Amiram Eldar_, Sep 19 2023

%p A006515 := proc(n) local i;

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

%p if (nops(numtheory[factorset](i)) < 3) then

%p return i

%p fi: end: seq(A006515(n), n=1..19);

%t Select[Array[2^Prime[#] - 1 &, 25], PrimeOmega@ # <= 2 &] (* _Michael De Vlieger_, May 04 2017 *)

%Y Cf. A000225, A001348, A006514.

%K nonn

%O 1,1

%A _N. J. A. Sloane_.

%E More terms from _Sean A. Irvine_, May 04 2017