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A334686
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Start with n, and successively apply phi, phi, sigma', phi, phi, sigma', phi, ... until reaching either 0 or 1; a(n) is the number of steps needed (phi = A000010, sigma' = A001065); or a(n) = -1 if 0 or 1 is never reached.
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5
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0, 1, 2, 2, 3, 2, 3, 3, 3, 3, 5, 3, 5, 3, 5, 5, 6, 3, 5, 5, 5, 5, 6, 5, 6, 5, 5, 5, 8, 5, 6, 6, 6, 6, 6, 5, 8, 5, 6, 6, 8, 5, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 8, 5, 8, 6, 8, 8, 8, 6, 8, 6, 8, 8, 8, 6, 8, 8, 8, 6, 8, 6, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 9, 6, 9, 8, 8, 8, 9, 6, 8, 8, 8, 6, 8, 8, 9, 8, 8, 8, 9, 8, 9, 8, 8, 8
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OFFSET
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1,3
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COMMENTS
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LINKS
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EXAMPLE
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The trajectory of n=7 is 7, 6, 2, 1, ... which takes three steps to reach 0 or 1, so a(7) = 3.
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MATHEMATICA
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A334686[n_]:=Module[{i=0}, NestWhile[If[Mod[i++, 3]==2, DivisorSigma[1, #]-#, EulerPhi[#]]&, n, #>1&]; i]; Array[A334686, 100] (* Paolo Xausa, Nov 16 2023 *)
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PROG
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(PARI) a(n) = { for (k=0, oo, if (n<=1, return (k), k%3==2, n=sigma(n)-n, n=eulerphi(n))) } \\ Rémy Sigrist, May 09 2020
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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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