login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Primes p such that 2^p-1 has exactly 3 distinct prime factors.
2

%I #5 May 22 2021 04:28:20

%S 29,43,47,53,71,73,79,179,193,211,257,277,283,311,331,349,353,389,409,

%T 443,467,499,563,577,599,613,631,643,647,683,709,751,769,829,919,941,

%U 1039,1103,1117,1123,1171,1193

%N Primes p such that 2^p-1 has exactly 3 distinct prime factors.

%C The corresponding Mersenne numbers are in A135977.

%C a(43) >= 1237.

%C The following primes are also terms of this sequence: 1301, 1303, 1327, 1459, 1531, 1559, 1907, 2311, 2383, 2887, 3041, 3547, 3833, 4127, 4507, 4871, 6883, 7673, 8233.

%F 2^a(n) - 1 = A135977(n).

%e 29 is a term since 2^29-1 = 536870911 = 233 * 1103 * 2089 has exactly 3 distinct prime factors.

%t Select[Range[200], PrimeQ[#] && PrimeNu[2^# - 1] == 3 &]

%Y Subsequence of A054723.

%Y Cf. A000225, A065341, A135975, A135976, A135977, A135978.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, May 21 2021