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%I #10 Oct 20 2024 03:34:52
%S 3,7,31,127,8191,131071,524287,2147483647,137438953471,2199023255551,
%T 8796093022207,9007199254740991,2305843009213693951,
%U 147573952589676412927,9444732965739290427391,158456325028528675187087900671,2535301200456458802993406410751
%N Numbers of the form 2^p - 1, where p is a prime number that is not the sum, minus 1, of a Pythagorean triple.
%C See A136003 for the values of p.
%H Amiram Eldar, <a href="/A136005/b136005.txt">Table of n, a(n) for n = 1..236</a>
%F a(n) = 2^A136003(n) - 1.
%e a(3) = 31 because A136003(3) = 5 and 2^5 = 32 and 32-1 = 31.
%t q[n_] := PrimeQ[n] && (n == 2 || Module[{d = Divisors[(n+1)/2]}, AllTrue[Range[3, Length[d]], d[[#]] >= 2 * d[[#-1]] &]]); 2^Select[Range[100], q] - 1 (* _Amiram Eldar_, Oct 20 2024 *)
%Y Cf. A000079, A000668, A136002, A136003.
%K nonn
%O 1,1
%A _Omar E. Pol_, Dec 17 2007
%E a(16)-a(17) from _Amiram Eldar_, Oct 20 2024