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

Author

Amiram Eldar, Sep 23 2021

Keywords

• nonn
• more

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.

Crossrefs

The unitary version of A328859.

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

Programs

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