A289127 Numbers k such that uphi(k)/uphi(uphi(k)) > uphi(m)/uphi(uphi(m)) for all m < k, where uphi is the unitary totient function (A047994).
1, 3, 7, 31, 211, 2311, 32048, 512768, 9737984, 300690391, 6915878971, 8626257644
Offset: 1
Links
- Paul Erdős and M. V. Subbarao, On the iterates of some arithmetic functions, The theory of arithmetic functions (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich. 1971), Lecture Notes in Math., 251, pp. 119-125, Springer, Berlin, 1972. [alternate link]
Programs
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Mathematica
uphi[n_] := If[n==1,1,(Times @@ (Table[ #[[1]]^ #[[2]] - 1, {1} ] & /@ FactorInteger[n]))[[1]]]; a = {}; k=1; rmax = 0; While[Length[a]<8,s = uphi[ k]; s2 = uphi[ s]; r = s/s2; If[r > rmax, AppendTo[a, k]; rmax = r]; k++]; a
Extensions
a(10)-a(12) from Amiram Eldar, Mar 26 2023