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

1,1

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

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 *)

Crossrefs

Cf. A005384, A043297.

Cf. A023212.

Sequence in context: A095080 A350179 A229289 * A360932 A291691 A178576

Adjacent sequences: A087631 A087632 A087633 * A087635 A087636 A087637

Keyword

nonn

Author

T. D. Noe, Oct 24 2003

Status

approved