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a(n) = gcd(sigma(n), phi(n)) - gcd(sigma(rad(n)), phi(rad(n))); rad = A007947.
6

%I #16 Oct 18 2019 00:07:15

%S 0,0,0,0,0,0,0,0,-1,0,0,2,0,0,0,0,0,1,0,0,0,0,0,2,-1,0,0,-2,0,0,0,0,0,

%T 0,0,-1,0,0,0,0,0,0,0,2,-2,0,0,2,1,-1,0,-4,0,4,0,18,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,1,0,0,-4,-2,0,0,0,0,-1,0,0,-4,0,0,0,18,0,-2,0,2,0,0,0,2,0,-3,8,-1,0,0,0,0,0,0,0,2,0,0,0,2,0,0,0,12,-6

%N a(n) = gcd(sigma(n), phi(n)) - gcd(sigma(rad(n)), phi(rad(n))); rad = A007947.

%H Charles R Greathouse IV, <a href="/A066087/b066087.txt">Table of n, a(n) for n = 1..10000</a>

%F A009223(n) - A066086(n) = gcd(sigma(n), phi(n)) - gcd(sigma(A007947(n)), phi(A007947(n))).

%t Table[GCD[DivisorSigma[1, n], EulerPhi@ n] - GCD[DivisorSigma[1, #], EulerPhi@ #] &[Times @@ FactorInteger[n][[All, 1]]], {n, 120}] (* _Michael De Vlieger_, Feb 19 2017 *)

%o (PARI) rad(f)=for(i=1,#f~,f[i,2]=1); f

%o g(f)=gcd(sigma(f),eulerphi(f))

%o a(n)=my(f=factor(n),k=rad(f)); g(f)-g(k) \\ _Charles R Greathouse IV_, Dec 09 2013

%Y Cf. A048250, A023900, A000203, A007947, A000010, A009223, A066086.

%K sign

%O 1,12

%A _Labos Elemer_, Dec 04 2001