A247071 Numbers n such that 2^n-1 has only one primitive prime factor, sorted according to the magnitude of the corresponding prime.

2, 4, 3, 10, 12, 8, 18, 5, 20, 14, 9, 7, 15, 24, 16, 30, 21, 22, 26, 42, 13, 34, 40, 32, 54, 17, 38, 27, 19, 33, 46, 56, 90, 78, 62, 31, 80

Offset: 1

Author

Eric Chen, Nov 16 2014

Keywords

• nonn
• more

Comments

Periods associated with A144755 in base 2. The binary analog of A051627.

Examples

			2^12 - 1 = 4095 = 3 * 3 * 5 * 7 * 13, but none of 3, 5, 7 is a primitive prime factor, so the only primitive prime factor of 2^12 - 1 is 13.
		

Crossrefs

Cf. A161508, A161509, A144755, A007498, A007615, A051627, A040017.

Programs

Mathematica

nmax = 65536; primesPeriods = Reap[Do[p = Cyclotomic[n, 2]/GCD[n, Cyclotomic[n, 2]]; If[PrimeQ[p], Print[n]; Sow[{p, n}]], {n, 1, nmax}]][[2, 1]]; Sort[primesPeriods][[All, 2]]

Formula

a(n) = A002326((A144755(n+1)-1)/2). - Max Alekseyev, Feb 11 2024

Extensions

Sequence trimmed to the established terms of A144755 by Max Alekseyev, Feb 11 2024