login
A269264
Numbers k such that (2^k-1)^2 - 2 is a semiprime.
3
5, 9, 13, 16, 23, 24, 28, 35, 37, 38, 40, 47, 48, 51, 52, 57, 61, 65, 67, 70, 79, 83, 84, 85, 88, 90, 102, 111, 144, 148, 157, 162, 168, 169, 177, 181, 190, 237, 246, 298, 308, 346
OFFSET
1,1
COMMENTS
a(43) >= 385. - Serge Batalov, Feb 26 2023
EXAMPLE
a(1) = 5 because 31^2-2 = 959 = 7*137 which is semiprime.
a(2) = 9 because 511^2-2 = 261119 = 23*11353 which is semiprime.
MATHEMATICA
Select[Range[120], PrimeOmega[(2^# - 1)^2 - 2] == 2 &]
PROG
(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];
(PARI) isok(n) = bigomega((2^n-1)^2-2) == 2; \\ Michel Marcus, Feb 22 2016
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Vincenzo Librandi, Feb 21 2016
EXTENSIONS
a(29)-a(42) from Hugo Pfoertner, Aug 05 2019
STATUS
approved