%I #10 May 15 2013 01:31:05
%S 3,28,108,2352,2544,7936,13632,26736,209904,256608,1394112,2052864,
%T 2169456,2490864,11942400,18884416,258072480,415272960,2064579840,
%U 3737456640,3963371520,4672512000
%N Numbers n such that phi(sigma(n)) + phi(phi(n)) = n.
%C If both (3^n-1)/2 and 2*3^n-1 are prime then 48*(2*3^n-1) is in the sequence (the proof is easy). So if n is in the intersection of A028491 and A003307 then 48*(2*3^n-1) is in this sequence. Conjecture: There exist only two such terms, namely 2544 and 209904.
%C If both (3^n*31-1)/2 and 2*3^n*31-1 are prime then 48*(2*3^n*31-1) is in the sequence (the proof is easy). Conjecture: There exist only three such terms, namely 26736, 2169456, and 26376103844085843261484656.
%e 18884416 is in the sequence because phi(sigma(18884416)) + phi(phi(18884416)) = 18884416.
%t Do[If[n == EulerPhi[DivisorSigma[1, n]] + EulerPhi[EulerPhi[n]], Print[n] ], {n, 10000000}]
%o (PARI) is(n)=eulerphi(sigma(n))+eulerphi(eulerphi(n))==n \\ _Charles R Greathouse IV_, Mar 06 2013
%Y Cf. A003307, A028491, A107652, A107653.
%K nonn
%O 1,1
%A _Farideh Firoozbakht_, May 26 2005
%E a(17)-a(22) from _Donovan Johnson_, Mar 06 2013