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ClearAll[PerfectTotientNumberQ]
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PerfectTotientNumberQ[n_Integer] := Total[Rest[Most[FixedPointList[EulerPhi, n]]]] == n
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res = {};
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i = 0;
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While[Length[res] < 20,
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i++;
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If[PerfectTotientNumberQ[i], AppendTo[res, i]]
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]
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res
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