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Numbers m which can be written as x*y with phi(x)*sigma(y) = m, where x and y are positive integers, phi(.) is Euler's totient function, and sigma(y) is the sum of all (positive) divisors of y.
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%I #10 Dec 22 2016 12:05:37

%S 1,6,12,18,24,48,54,56,84,96,112,120,162,168,192,224,240,252,336,360,

%T 384,448,468,480,486,588,600,672,720,756,768,896,936,960,992,1080,

%U 1176,1200,1344,1440,1458,1536,1764,1792,1800,1872,1920,1984,2160,2268

%N Numbers m which can be written as x*y with phi(x)*sigma(y) = m, where x and y are positive integers, phi(.) is Euler's totient function, and sigma(y) is the sum of all (positive) divisors of y.

%C As phi(x) is even for any integer x > 1, only the first term 1 is odd.

%C If n is a perfect number, then 2*n = phi(2)*sigma(n) is a term of the sequence.

%H Zhi-Wei Sun, <a href="/A279894/b279894.txt">Table of n, a(n) for n = 1..1000</a>

%e a(2) = 6 since 6 = 3*2 with phi(3)*sigma(2) = 6.

%e a(3) = 12 since 12 = 2*6 with phi(2)*sigma(6) = 12.

%t sigma[n_]:=sigma[n]=DivisorSigma[1,n];

%t phi[n_]:=phi[n]=EulerPhi[n];

%t Dv[m_]:=Dv[m]=Divisors[m];

%t Ld[m_]:=Ld[m]=Length[Dv[m]];

%t n=0;Do[Do[If[sigma[Part[Dv[m],i]]phi[m/Part[Dv[m],i]]==m,n=n+1;Print[n," ",m];Goto[aa]],{i,1,Ld[m]}];Label[aa];Continue,{m,1,2300}]

%Y Cf. A000010, A000203, A000396.

%K nonn

%O 1,2

%A _Zhi-Wei Sun_, Dec 22 2016