cp's OEIS Frontend

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.

%I A348003 #4 Sep 24 2021 09:05:33
%S A348003 1,2,546,2730,13650,101010,199290,996450,1919190,7373730,28020174,
%T A348003 32626230,125353410,140100870,700504350,2381714790,11908573950,
%U A348003 15270994830
%N 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.
%C A348003 The maximal possible value of the ratio A348001(k)/A034444(k) is 1 which occurs at the terms of A348004.
%C A348003 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, ...
%C A348003 a(19) > 2*10^10, if it exists.
%t A348003 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
%Y A348003 The unitary version of A328859.
%Y A348003 Cf. A034444, A047994, A348001, A348002, A348004.
%K A348003 nonn,more
%O A348003 1,2
%A A348003 _Amiram Eldar_, Sep 23 2021