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

1,1

Comments

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

Links

Table of n, a(n) for n=1..37.

Formula

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

Example

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.

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]]

Crossrefs

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

Sequence in context: A208324 A277416 A064691 * A014664 A270600 A350231

Adjacent sequences: A247068 A247069 A247070 * A247072 A247073 A247074

Keyword

nonn,more

Author

Eric Chen, Nov 16 2014

Extensions

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

Status

approved