A348174 Indices k of records of low value in the ratios A348173(k)/k.

1, 2, 546, 2730, 13650, 51870, 101010, 199290, 505050, 881790, 996450, 1919190, 32626230, 140100870, 654443790, 865554690

Offset: 1

Author

Amiram Eldar, Oct 04 2021

Keywords

• nonn
• more

Comments

The maximal possible value of the ratio A348173(k)/k is 1 which occurs at the terms of A348004.

The rounded values of the corresponding records are 1, 0.5, 0.478, 0.469, 0.466, 0.465, 0.4642, 0.4638, 0.4621, 0.4620, 0.460, 0.453, 0.450, 0.447, 0.446, 0.445, ...

a(17) > 1.4*10^9.

Crossrefs

The unitary version of A348159.

Cf. A348003, A348004, A348173.

Programs

Mathematica

f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; r[n_] := Plus @@ DeleteDuplicates[uphi /@ Select[Divisors[n], CoprimeQ[#, n/#] &]]/n; rm = 2; seq = {}; Do[r1 = r[n]; If[r1 < rm, rm = r1; AppendTo[seq, n]], {n, 1, 2*10^5}]; seq