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.

1, 2, 546, 2730, 13650, 101010, 199290, 996450, 1919190, 7373730, 28020174, 32626230, 125353410, 140100870, 700504350, 2381714790, 11908573950, 15270994830

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

Table of n, a(n) for n=1..18.

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.

Cf. A034444, A047994, A348001, A348002, A348004.

Sequence in context: A119780 A120840 A348174 * A058429 A336784 A201247

Adjacent sequences: A348000 A348001 A348002 * A348004 A348005 A348006

Keyword

nonn,more

Author

Amiram Eldar, Sep 23 2021

Status

approved