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Primes p of the form 4k+3 where sigma(phi(sigma(p)))= phi(sigma(phi(p))).
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%I #5 Mar 30 2012 17:37:43

%S 114190259,6364631939,10296994891,10429820759

%N Primes p of the form 4k+3 where sigma(phi(sigma(p)))= phi(sigma(phi(p))).

%C Between the first 480000000 primes, the equation (*): sigma(phi(sigma(x)))=phi(sigma(phi(x))) has 256 solutions q(i) and only four of them namely q(76),q(215),q(254) and q(256) are of the form 4k+3. Sequence A112017 gives composite solutions of the equation (*), which are of the form 4k+3.

%t Do[If[Mod[Prime[m], 4]==3 && DivisorSigma[1, EulerPhi[Prime[m]+1 ==EulerPhi[DivisorSigma[1, Prime[m]-1]], Print[Prime[m]]], {m, 480000000}]

%Y Cf. A112017.

%K more,nonn

%O 1,1

%A _Farideh Firoozbakht_, Sep 15 2005