%I #26 Mar 06 2023 02:49:00

%S 5,9,13,16,23,24,28,35,37,38,40,47,48,51,52,57,61,65,67,70,79,83,84,

%T 85,88,90,102,111,144,148,157,162,168,169,177,181,190,237,246,298,308,

%U 346

%N Numbers k such that (2^k-1)^2 - 2 is a semiprime.

%C a(43) >= 385. - _Serge Batalov_, Feb 26 2023

%H factordb.com, <a href="http://factordb.com/index.php?query=%282%5E385-1%29%5E2-2">Status of (2^385-1)^2-2</a>.

%e a(1) = 5 because 31^2-2 = 959 = 7*137 which is semiprime.

%e a(2) = 9 because 511^2-2 = 261119 = 23*11353 which is semiprime.

%t Select[Range[120], PrimeOmega[(2^# - 1)^2 - 2] == 2 &]

%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..120]| IsSemiprime(s) where s is (2^n-1)^2-2];

%o (PARI) isok(n) = bigomega((2^n-1)^2-2) == 2; \\ _Michel Marcus_, Feb 22 2016

%Y Cf. A091515, A091516, A268574, A360993, A360994.

%K nonn,more,hard

%O 1,1

%A _Vincenzo Librandi_, Feb 21 2016

%E a(29)-a(42) from _Hugo Pfoertner_, Aug 05 2019