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

2, 3, 5, 7, 11, 13, 23, 29, 37, 41, 43, 53, 67, 73, 79, 83, 89, 97, 113, 127, 131, 139, 163, 173, 179, 191, 193, 199, 233, 239, 251, 277, 281, 293, 307, 359, 373, 409, 419, 431, 433, 443, 487, 491, 499, 509, 577, 593, 619, 641, 653, 659, 673, 683, 709, 719, 727

Offset: 1

Author

T. D. Noe, Oct 24 2003

Keywords

• nonn

Comments

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

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

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 1..2000
• Eric Weisstein's World of Mathematics, Totient Function

Crossrefs

Cf. A005384, A043297.

Cf. A023212.

Programs

Mathematica

t=Table[EulerPhi[n], {n, 3, 20000}]; Union[Select[t, Mod[ #, 4]==0&&PrimeQ[ #/4]&& #/4<1000&]/4] (* or *)
Select[Prime[Range[100]],PrimeQ[4#+1]||PrimeQ[2#+1]&] (* Enrique Pérez Herrero, Aug 16 2011 *)