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A348264
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a(n) is the number of iterations that n requires to reach a fixed point under the map x -> A348173(x).
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2
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0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0
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OFFSET
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1,84
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COMMENTS
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a(n) first differs from A011765(n+2) at n = 84.
The fixed points are terms of A348004, so a(n) = 0 if and only if n is a term of A348004.
Conjecture: essentially partial sums of A219977 (verified for n <= 5000).
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LINKS
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EXAMPLE
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a(2) = 1 since there is one iteration of the map x -> A348173(x) starting from 2: 2 -> 1.
a(84) = 2 since there are 2 iterations of the map x -> A348173(x) starting from 84: 84 -> 78 -> 39.
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MATHEMATICA
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f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := Plus @@ DeleteDuplicates[uphi /@ Select[Divisors[n], CoprimeQ[#, n/#] &]]; a[n_] := -2 + Length@ FixedPointList[s, n]; Array[a, 100]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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