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 A065966 Numbers k such that phi(k) / 2 is prime. 10
 5, 7, 8, 9, 10, 11, 12, 14, 18, 22, 23, 46, 47, 59, 83, 94, 107, 118, 166, 167, 179, 214, 227, 263, 334, 347, 358, 359, 383, 454, 467, 479, 503, 526, 563, 587, 694, 718, 719, 766, 839, 863, 887, 934, 958, 983, 1006, 1019, 1126, 1174, 1187, 1283, 1307, 1319 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is probably an infinite sequence, but a proof would be nice. Are there infinitely many consecutive terms of the sequence which are also consecutive integers? (For example, 7, 8 and 46, 47.) Apart from 8, 9, 12 and 18, all the terms of the sequence are safe primes or twice safe primes. It is not known if there are infinitely many safe primes (cf. A005385, A005384). For consecutive terms of the sequence which are also consecutive integers see A066179. - Vladeta Jovovic, Dec 16 2001 LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 AndrÃ© HernÃ¡ndez-Espiet, Reyes M. Ortiz-Albino, On the Characterization of tau(n)-Atoms, arXiv:1905.02834 [math.NT], 2019. See Proposition 3.1. FORMULA Numbers k such that A068212(k) = 2. EXAMPLE phi(46)/2 = 22/2 = 11, a prime. MATHEMATICA Select[Range[1400], PrimeQ[EulerPhi[#]/2]&] (* Harvey P. Dale, Feb 11 2020 *) PROG (PARI) for(n=3, 5000, if(isprime(eulerphi(n)/2), print1(n, ", "))) (PARI) { n=0; for (m=3, 10^9, if (isprime(eulerphi(m)/2), write("b065966.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Nov 05 2009 CROSSREFS Cf. A000010, A005385, A005384, A066179, A006530, A052126, A068211, A068212. Sequence in context: A242963 A191846 A068213 * A096989 A031950 A043694 Adjacent sequences:  A065963 A065964 A065965 * A065967 A065968 A065969 KEYWORD nonn AUTHOR Joseph L. Pe, Dec 08 2001 EXTENSIONS More terms from Jason Earls, Dec 09 2001 Edited by Charles R Greathouse IV, Mar 18 2010 STATUS approved

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)