A136005 Numbers of the form 2^p - 1, where p is a prime number that is not the sum, minus 1, of a Pythagorean triple.

3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 137438953471, 2199023255551, 8796093022207, 9007199254740991, 2305843009213693951, 147573952589676412927, 9444732965739290427391, 158456325028528675187087900671, 2535301200456458802993406410751

Offset: 1

Author

Omar E. Pol, Dec 17 2007

Keywords

• nonn

Comments

See A136003 for the values of p.

Examples

			a(3) = 31 because A136003(3) = 5 and 2^5 = 32 and 32-1 = 31.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..236

Crossrefs

Cf. A000079, A000668, A136002, A136003.

Programs

Mathematica

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 *)

Formula

a(n) = 2^A136003(n) - 1.

Extensions

a(16)-a(17) from Amiram Eldar, Oct 20 2024