A328859 Indices k of records of low value in the ratios A319696(k)/A000005(k) between the number of distinct values of the Euler totient function applied to the divisors of k and the number of divisors of k.

1, 2, 60, 120, 240, 480, 960, 1920, 3840, 4080, 8160, 16320, 32640, 65280, 130560, 261120, 522240, 1044480, 1485120, 2227680, 2970240, 4455360, 8910720, 17821440, 35642880, 42325920, 63488880, 69090840, 84651840, 126977760, 169303680, 253955520, 507911040, 761866560

Offset: 1

Author

Amiram Eldar, Oct 28 2019

Keywords

• nonn

Comments

The maximal possible value of the ratio A319696(k)/A000005(k) is 1 which occurs at the terms of A326835.

The rounded values of the corresponding ratios are 1, 0.5, 0.417, 0.375, 0.35, 0.333, 0.321, 0.313, 0.306, 0.275, 0.25, 0.232, 0.219, 0.208, 0.2, 0.193, 0.188, 0.183, 0.179, 0.170, 0.168, 0.158, 0.148, 0.141, 0.135, 0.132, 0.130, 0.129, 0.122, 0.117, 0.115, 0.108, 0.102, 0.101, ...

Crossrefs

Cf. A000010, A102190, A319696, A326835.

Programs

Mathematica

r[n_] := Length @ Union[EulerPhi /@ (d = Divisors[n])]/Length[d]; rm = 2; s = {}; Do[r1 = r[n]; If[r1 < rm, rm = r1; AppendTo[s, n]], {n, 1, 10^5}]; s