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Numbers n such that phi(n) + sigma(n) is the mean value of phi(sigma(n)) and sigma(phi(n)).
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%I #18 Jan 16 2020 18:13:47

%S 46427,66929,1560793,1796647,1810601,1839673,2053781,2176673,2426063,

%T 2467007,3172013,3898603,4208939,12011921,19504309,29241797,35464241,

%U 35501573,46838431,46976227,66580381,69406561,88015273,104722321

%N Numbers n such that phi(n) + sigma(n) is the mean value of phi(sigma(n)) and sigma(phi(n)).

%C All terms below 110000000 are odd and squarefree. What is the smallest term of other form?

%C a(28) = 233187611 = 31^2 * 167 * 1453 is the first nonsquarefree term. - _Charles R Greathouse IV_, Oct 17 2013

%H Charles R Greathouse IV and Donovan Johnson, <a href="/A230237/b230237.txt">Table of n, a(n) for n = 1..119</a> (terms < 3*10^10, first 88 terms from Charles R Greathouse IV)

%t Do[If[2(DivisorSigma[1,n]+EulerPhi[n])==EulerPhi[DivisorSigma[1,n]]+DivisorSigma[1,EulerPhi[n]],Print[n]],{n,110000000}]

%t Select[Range[1048*10^5],EulerPhi[#]+DivisorSigma[1,#]==Mean[{EulerPhi[ DivisorSigma[ 1,#]],DivisorSigma[ 1,EulerPhi[ #]]}]&] (* _Harvey P. Dale_, Jan 16 2020 *)

%o (PARI) for(n=1,1e8, f=factor(n); ph=eulerphi(f); s=sigma(f); if(2*ph+2*s == sigma(ph)+eulerphi(s), print1(n", "))) \\ _Charles R Greathouse IV_, Oct 17 2013

%Y Cf. A000010, A000203, A062401, A062402, A230238.

%K nonn

%O 1,1

%A _Farideh Firoozbakht_, Oct 16 2013