cp's OEIS Frontend

A360993 Numbers k such that (2^k - 1)^3 + 2 is a semiprime.

%I A360993 #30 Mar 03 2023 13:56:07
%S A360993 4,5,8,12,13,18,20,29,38,56,60,62,76,82,101,118,202,210,230,276,328,
%T A360993 332,336,338,368
%N A360993 Numbers k such that (2^k - 1)^3 + 2 is a semiprime.
%C A360993 a(26) >= 406.
%C A360993 438, 500, 526, 604, 648, 696 are also in this sequence, but their positions cannot be established before finding any factor for the values corresponding to the following "blockers": 406, 496, 528.
%C A360993 2382, 2733, 2910, 3368, 3508, 5338, 7705, 11185, 19905, 23814, 38545, 179294 are larger terms of this sequence, but their positions cannot be established. These produce "trivial" semiprimes where one prime is small (e.g., 3 or 11).
%H A360993 factordb.com, <a href="http://factordb.com/index.php?query=%282%5E406-1%29%5E3%2B2">Status of (2^406-1)^3+2</a>.
%e A360993 a(1) = 4 because 15^3 + 2 = 3377 = 11 * 307, which is semiprime.
%e A360993 a(2) = 5 because 31^3 + 2 = 29793 = 3 * 9931, which is semiprime.
%t A360993 Select[Range[70], PrimeOmega[(2^# - 1)^3 - 2] == 2 &]
%o A360993 (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..70]| IsSemiprime(s) where s is (2^n-1)^3+2];
%o A360993 (PARI) isok(n) = bigomega((2^n-1)^3+2) == 2;
%Y A360993 Cf. A091515, A091516, A100899, A100900, A268574, A269264, A360994.
%K A360993 nonn,more,hard
%O A360993 1,1
%A A360993 _Serge Batalov_, Feb 27 2023
%E A360993 a(20)-a(26) from _Serge Batalov_, Mar 03 2023