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 A161508 Numbers k such that 2^k-1 has only one primitive prime factor. 9
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 16 05:56 EDT 2022. Contains 353693 sequences. (Running on oeis4.)