A161508 Numbers k such that 2^k-1 has only one primitive prime factor.

2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 27, 30, 31, 32, 33, 34, 38, 40, 42, 46, 49, 54, 56, 61, 62, 65, 69, 77, 78, 80, 85, 86, 89, 90, 93, 98, 107, 120, 122, 126, 127, 129, 133, 145, 147, 150, 158, 165, 170, 174, 184, 192, 195, 202, 208

Offset

1,1

Comments

Also, numbers k such that A086251(k) = 1.

Also, numbers k such that A064078(k) is a prime power.

The corresponding primitive primes are listed in A161509.

The binary expansion of 1/p has period k and this is the only prime with such a period. The binary analog of A007498.

This sequence has many terms in common with A072226. A072226 has the additional term 6; but it does not have terms 18, 20, 21, 54, 147, 342, 602, and 889 (less than 10000).

All known terms that are not in A072226 belong to A333973.

Links

T. D. Noe, Table of n, a(n) for n=1..179

Wikipedia, Unique prime, section Binary unique primes.

Mathematica

Select[Range[1000], PrimePowerQ[Cyclotomic[ #, 2]/GCD[Cyclotomic[ #, 2], # ]]&]

Prog

(PARI) is_A161508(n) = my(t=polcyclo(n, 2)); isprimepower(t/gcd(t, n)); \\ Charles R Greathouse IV, Nov 17 2014

Crossrefs

Cf. A007498, A064078, A072226, A086251, A144755, A161509, A247071, A333973.

Sequence in context: A324766 A336621 A039224 * A039264 A231004 A039161

Adjacent sequences: A161505 A161506 A161507 * A161509 A161510 A161511

Keyword

nonn

Author

T. D. Noe, Jun 17 2009

Status

approved