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%I #37 Mar 06 2023 02:13:22
%S 4,6,7,10,11,14,22,36,38,39,44,45,48,49,60,72,74,75,89,92,96,99,105,
%T 110,111,113,116,131,138,143,150,170,173,182,194,201,212,234,260,282,
%U 300,317,335,341,345,383,405
%N Numbers k such that (2^k + 1)^2 - 2 is a semiprime.
%C a(48) >= 428. - _Serge Batalov_, Feb 25 2023
%H factordb.com, <a href="http://factordb.com/index.php?query=%282%5E428%2B1%29%5E2-2">Status of (2^428+1)^2-2</a>.
%e a(1) = 4 because 17^2 - 2 = 287 = 7*41, which is semiprime.
%e a(2) = 6 because 65^2 - 2 = 4223 = 41*103, which is semiprime.
%t Select[Range[105], PrimeOmega[(2^# + 1)^2 - 2] == 2 &]
%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [1..110]| 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. A091513, A091514, A093069, A269264, A360993, A360994.
%K nonn,more,hard
%O 1,1
%A _Vincenzo Librandi_, Feb 21 2016
%E a(25)-a(39) from _Hugo Pfoertner_, Aug 05 2019
%E a(40)-a(41) from chris2be8@yahoo.com, Feb 25 2023
%E a(42)-a(47) from _Serge Batalov_, Feb 26 2023
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