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A087634 Primes p such that the equation phi(x) = 4p has a solution, where phi is the totient function. 3

%I

%S 2,3,5,7,11,13,23,29,37,41,43,53,67,73,79,83,89,97,113,127,131,139,

%T 163,173,179,191,193,199,233,239,251,277,281,293,307,359,373,409,419,

%U 431,433,443,487,491,499,509,577,593,619,641,653,659,673,683,709,719,727

%N Primes p such that the equation phi(x) = 4p has a solution, where phi is the totient function.

%C Except for p=2, the complement of A043297. Note that for primes p < 1000, we need to check for solutions x < 18478. The equation phi(x) = 2p has solutions for Sophie Germain primes, A005384

%C a(n) is also the primes p with 2p+1 or 4p+1 also prime, sequences A005384 and A023212. For the case 2p+1 a trivial solution is phi(6p+3)=4p, and for 4p+1, phi(4p+1)=4p. - _Enrique Pérez Herrero_, Aug 16 2011

%H Enrique Pérez Herrero, <a href="/A087634/b087634.txt">Table of n, a(n) for n = 1..2000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>

%t t=Table[EulerPhi[n], {n, 3, 20000}]; Union[Select[t, Mod[ #, 4]==0&&PrimeQ[ #/4]&& #/4<1000&]/4] (* or *)

%t Select[Prime[Range[100]],PrimeQ[4#+1]||PrimeQ[2#+1]&] (* _Enrique Pérez Herrero_, Aug 16 2011 *)

%Y Cf. A005384, A043297.

%Y Cf. A023212.

%K nonn

%O 1,1

%A _T. D. Noe_, Oct 24 2003

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Last modified May 15 13:52 EDT 2021. Contains 343920 sequences. (Running on oeis4.)