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%I #13 Sep 20 2014 05:07:28
%S 827,975,1607,13149,20919,34921,58649,202223,347869,545377,900521,
%T 1451135,2288845,2453509,2804855,3063031,4134579,11320177,11446955,
%U 14573651,16477307,17678225,25164429,27514643,28475077,47443799,49348333,50971501,53108173,66213757
%N Numbers n such that phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = sigma(n).
%H Hiroaki Yamanouchi, <a href="/A066946/b066946.txt">Table of n, a(n) for n = 1..54</a>
%e Let n = 827. Then phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = phi(826) + sigma(828) - phi(828) - sigma(826) = 348 + 2184 - 264 - 1440 = 828 = sigma(n), so 827 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==b]; Do[If[g[n]==True, Print[n]], {n, 1, 10^5}]
%Y Cf. A000010, A000203, A066850, A066939, A066945.
%K nonn
%O 1,1
%A _Joseph L. Pe_, Jan 24 2002
%E Edited by _Dean Hickerson_ and _Robert G. Wilson v_, Jan 26 2002
%E a(23)-a(26) from _Donovan Johnson_, Jan 02 2009
%E a(27)-a(30) from _Hiroaki Yamanouchi_, Sep 20 2014
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