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A348003 Indices k of records of low value of the ratios A348001(k)/A034444(k) between the number of distinct values of the unitary totient function applied to the unitary divisors of k and the number of unitary divisors of k. 2
1, 2, 546, 2730, 13650, 101010, 199290, 996450, 1919190, 7373730, 28020174, 32626230, 125353410, 140100870, 700504350, 2381714790, 11908573950, 15270994830 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The maximal possible value of the ratio A348001(k)/A034444(k) is 1 which occurs at the terms of A348004.
The rounded values of the corresponding record values are 1, 0.5, 0.438, 0.406, 0.375, 0.359, 0.344, 0.312, 0.281, 0.266, 0.258, 0.250, 0.242, 0.199, 0.195, 0.170, 0.168, 0.145, ...
a(19) > 2*10^10, if it exists.
LINKS
MATHEMATICA
f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; r[n_] := Length @ Union[uphi /@ (d = Select[Divisors[n], CoprimeQ[#, n/#] &])]/Length[d]; rm = 2; seq = {}; Do[r1 = r[n]; If[r1 < rm, rm = r1; AppendTo[seq, n]], {n, 1, 10^5}]; seq
CROSSREFS
The unitary version of A328859.
Sequence in context: A119780 A120840 A348174 * A058429 A336784 A201247
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Sep 23 2021
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)