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A076487
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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.
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1
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1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 77, 78, 79, 80, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..72.
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EXAMPLE
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If n is squarefree, then it is here. n=20: sigma[20]=42,phi[20]=8, GCD[42,8]=2, core[20]=10, sigma[10]=18,phi[10]=4, GCD[18,4]=2, so A009223[20]=A060086[20]=2.
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MATHEMATICA
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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], Print[n]], {n, 1, 256}]
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CROSSREFS
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Cf. A066086, A066087, A048250, A023900, A000203, A007947, A000010, A009223, A076485, A076486.
Sequence in context: A028826 A131565 A039218 * A181709 A033106 A119485
Adjacent sequences: A076484 A076485 A076486 * A076488 A076489 A076490
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 17 2002
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STATUS
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approved
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