%I #15 Dec 25 2015 00:03:11

%S 11,11063,11943,38585,39995,43021,63349,67709,967393,1267511,2020925,

%T 2915307,5805559,6584747,6659429,8064017,26260385,27681847,31886881,

%U 41932769,48922307,61270145,71429011,89087903,91364345,191945623

%N Numbers n such that phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = phi(n).

%H Harry J. Smith, <a href="/A066945/b066945.txt">Table of n, a(n) for n = 1..39</a>

%e Let n = 11. Then phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = phi(10) + sigma(12) - phi(12) - sigma(10) = 4 + 28 - 4 - 18 = 10 = phi(n), so 11 is in the sequence.

%t g[x_] := Module[{a, b, c, d, e, f}, a=EulerPhi[x]; b=DivisorSigma[1, x]; c=EulerPhi[a]; d=DivisorSigma[1, b]; e=EulerPhi[b]; f=DivisorSigma[1, a]; c+d-e-f==a]; Do[If[g[n]==True, Print[n]], {n, 1, 10^5}]

%o (PARI) { n=0; for (m=1, 10^10, e=eulerphi(m); s=sigma(m); if (eulerphi(e) + sigma(s) - eulerphi(s) - sigma(e) == e, write("b066945.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Apr 11 2010

%Y Cf. A000010, A000203, A066850, A066939, A066946.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Jan 24 2002

%E Edited by _Dean Hickerson_, Jan 26 2002

%E a(17)-a(26) from _Donovan Johnson_, Jan 02 2009