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%I #15 Aug 18 2019 04:30:59
%S 4,8,16,20,27,32,40,60,63,64,68,80,104,120,126,128,136,160,164,171,
%T 189,204,212,220,232,240,243,256,260,272,279,294,296,312,315,320,340,
%U 342,343,350,351,356,363,375,378,387,404,408,416,424,464,476,480,492,512
%N Nonsquarefree solutions to gcd(sigma(x), phi(x)) = gcd(sigma(core(x)), Phi(core(x))), i.e., when A009223(x) = A066086 or if A066087(x)=0 and mu(x)=0.
%H Amiram Eldar, <a href="/A076488/b076488.txt">Table of n, a(n) for n = 1..10000</a>
%e n=60: sigma(60)=168, phi(60)=16, gcd(168,16)=8, core(60)=30, sigma(30)=72, phi(30)=8, gcd(72,8)=8, so A009223(60)=A060086(60)=8.
%t ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] cor[x_] := Apply[Times, ba[x]] g1[x_] := GCD[DivisorSigma[1, x], EulerPhi[x]] g2[x_] := GCD[DivisorSigma[1, cor[x]], EulerPhi[cor[x]]] Do[s1=g1[n]; s2=g2[n]; If[Equal[s2, s1]&&Equal[MoebiusMu[n], 0], Print[n]], {n, 1, 1024}]
%Y Cf. A066086, A066087, A048250, A023900, A000203, A007947, A000010, A009223, A076485-A076487.
%K nonn
%O 1,1
%A _Labos Elemer_, Oct 17 2002
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