

A087634


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


3



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
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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: A075430 A095080 A229289 * A291691 A178576 A038970
Adjacent sequences: A087631 A087632 A087633 * A087635 A087636 A087637


KEYWORD

nonn


AUTHOR

T. D. Noe, Oct 24 2003


STATUS

approved



