A183077 Numbers of the form 2^p - 1, with p prime, for which each prime divisor has the form 4j + 3.

3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 8796093022207, 2305843009213693951, 604462909807314587353087, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727

Offset: 1

Author

Stuart Clary, Dec 23 2010

Keywords

• nonn
• hard

Comments

The Mersenne primes (A000668) are contained in this sequence.

Needed factorizations are in the Cunningham Project.

Examples

			8796093022207 = 2^43 - 1 = 431 * 9719 * 2099863.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..26
• S. S. Wagstaff, Jr., The Cunningham Project.

Crossrefs

Cf. A000668, A136005, A183075, A183076, A183078.

Cf. A000043, A136003, A183071, A183072, A183073, A183074.

Formula

a(n) = 2^A183073(n) - 1.