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A286067
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Unitary perfect totient numbers: numbers n that equal to the sum of their iterated unitary totient uphi(n).
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5
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OFFSET
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1,1
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COMMENTS
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The unitary version of A082897 (perfect totient numbers), in which the unitary totient function uphi(n) (A047994) replaces the Euler totient function phi(n) (A000010).
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LINKS
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EXAMPLE
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3910 is a unitary perfect totient number because 3910 = uphi(3910) + uphi(uphi(3910)) + uphi(uphi(uphi(3910))) + ... = 1408 + 1270 + 504 + 336 + 180 + 96 + 62 + 30 + 8 + 7 + 6 + 2 + 1.
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MATHEMATICA
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uphi[n_] := (Times @@ (Table[#[[1]]^#[[2]] - 1, {1}] & /@ FactorInteger[n]))[[1]]; kmax = 10000; a = Table[0, {kmax}]; uptns = {}; Do[e = uphi[k]; a[[k]] = e + a[[e]]; If[k == a[[k]], AppendTo[uptns , k]], {k, 2, kmax}]; uptns
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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