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A076488
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Non-squarefree 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.
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0
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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; internal format)
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OFFSET
| 1,1
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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.
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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}]
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CROSSREFS
| Cf. A066086, A066087, A048250, A023900, A000203, A007947, A000010, A009223, A076485-A076487.
Sequence in context: A104235 A143718 A031399 * A092259 A036693 A181471
Adjacent sequences: A076485 A076486 A076487 * A076489 A076490 A076491
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Oct 17 2002
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