A268574 Numbers k such that (2^k + 1)^2 - 2 is a semiprime.

4, 6, 7, 10, 11, 14, 22, 36, 38, 39, 44, 45, 48, 49, 60, 72, 74, 75, 89, 92, 96, 99, 105, 110, 111, 113, 116, 131, 138, 143, 150, 170, 173, 182, 194, 201, 212, 234, 260, 282, 300, 317, 335, 341, 345, 383, 405

Offset

1,1

Comments

a(48) >= 428. - Serge Batalov, Feb 25 2023

Links

Table of n, a(n) for n=1..47.

factordb.com, Status of (2^428+1)^2-2.

Example

a(1) = 4 because 17^2 - 2 = 287 = 7*41, which is semiprime.
a(2) = 6 because 65^2 - 2 = 4223 = 41*103, which is semiprime.

Mathematica

Select[Range[105], PrimeOmega[(2^# + 1)^2 - 2] == 2 &]

Prog

(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];
(PARI) isok(n) = bigomega((2^n+1)^2-2) == 2; \\ Michel Marcus, Feb 22 2016

Crossrefs

Cf. A091513, A091514, A093069, A269264, A360993, A360994.

Sequence in context: A032785 A096887 A340161 * A023631 A080641 A272632

Adjacent sequences: A268571 A268572 A268573 * A268575 A268576 A268577

Keyword

nonn,more,hard

Author

Vincenzo Librandi, Feb 21 2016

Extensions

a(25)-a(39) from Hugo Pfoertner, Aug 05 2019

a(40)-a(41) from chris2be8@yahoo.com, Feb 25 2023

a(42)-a(47) from Serge Batalov, Feb 26 2023

Status

approved