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%I #11 Dec 24 2015 23:52:56
%S 1,4,2669,9559,15293,32583,36593,38443,255367,257239,273977,283391,
%T 314101,421553,488363,532975,768699,839973,871757,1960479,2337221,
%U 2374867,3084659,3326653,3735029,4440017,5387373,7930439,8114377
%N Numbers n such that phi(phi(n)) + sigma(sigma(n)) = phi(sigma(n)) + sigma(phi(n)), where phi=A000010 is Euler's totient function and sigma=A000203 is the sum of divisors function.
%H Harry J. Smith, <a href="/A066850/b066850.txt">Table of n, a(n) for n = 1..114</a>
%e Let n = 2669. Then phi(phi(n)) + sigma(sigma(n)) = phi(2496) + sigma(2844) = 768 + 7280 = 8048 and phi(sigma(n)) + sigma(phi(n)) = phi(2844) + sigma(2496) = 936 + 7112 = 8048. So 2669 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]; Do[If[g[n] == 0, Print[n]], {n, 1, 10^6}]
%o (PARI) { n=0; for (m=1, 10^10, e=eulerphi(m); s=sigma(m); if (eulerphi(e) + sigma(s) == eulerphi(s) + sigma(e), write("b066850.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Apr 02 2010
%K nonn
%O 1,2
%A _Joseph L. Pe_, Jan 24 2002
%E Edited by _Dean Hickerson_, Jan 24 2002
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