A161508 - OEIS

%I #16 Oct 26 2020 23:00:41

%S 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,

%T 33,34,38,40,42,46,49,54,56,61,62,65,69,77,78,80,85,86,89,90,93,98,

%U 107,120,122,126,127,129,133,145,147,150,158,165,170,174,184,192,195,202,208

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

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

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

%C The corresponding primitive primes are listed in A161509.

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

%C 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).

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

%H T. D. Noe, <a href="/A161508/b161508.txt">Table of n, a(n) for n=1..179</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Unique_prime#Binary_unique_primes">Unique prime, section Binary unique primes</a>.

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

%o (PARI) is_A161508(n) = my(t=polcyclo(n,2)); isprimepower(t/gcd(t,n)); \\ _Charles R Greathouse IV_, Nov 17 2014

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

%K nonn

%O 1,1

%A _T. D. Noe_, Jun 17 2009