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 A076488 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. 1
 4, 8, 16, 20, 27, 32, 40, 60, 63, 64, 68, 80, 104, 120, 126, 128, 136, 160, 164, 171, 189, 204, 212, 220, 232, 240, 243, 256, 260, 272, 279, 294, 296, 312, 315, 320, 340, 342, 343, 350, 351, 356, 363, 375, 378, 387, 404, 408, 416, 424, 464, 476, 480, 492, 512 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 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. MATHEMATICA 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}] CROSSREFS Cf. A066086, A066087, A048250, A023900, A000203, A007947, A000010, A009223, A076485-A076487. Sequence in context: A312800 A312801 A312802 * A312803 A312804 A306199 Adjacent sequences:  A076485 A076486 A076487 * A076489 A076490 A076491 KEYWORD nonn AUTHOR Labos Elemer, Oct 17 2002 STATUS approved

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Last modified July 29 11:53 EDT 2021. Contains 346346 sequences. (Running on oeis4.)