A361968 Unitary highly totient numbers: numbers k that have more solutions x to the equation uphi(x) = k than any smaller k, where uphi is the unitary totient function (A047994).

1, 6, 8, 12, 24, 48, 96, 120, 144, 240, 480, 576, 720, 1440, 2880, 4320, 5760, 8640, 10080, 17280, 20160, 30240, 34560, 40320, 60480, 80640, 120960, 241920, 362880, 483840, 725760, 967680, 1209600, 1451520, 2177280, 2419200, 2903040, 3628800, 4354560, 4838400

Offset: 1

Author

Amiram Eldar, Apr 01 2023

Keywords

• nonn

Comments

Indices of records of A361967.

The corresponding numbers of solutions are 2, 3, 4, 5, 8, 11, ... (A361971).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..51

Crossrefs

The unitary version of A097942.

Cf. A047994, A135347, A347771, A361966, A361967, A361969, A361970, A361971.

Programs

Mathematica

solnum[n_] :=  Length[invUPhi[n]]; seq[kmax_] := Module[{s = {}, solmax=0}, Do[sol = solnum[k]; If[sol > solmax, solmax = sol; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[10^5] (* using the function invUPhi from A361966 *)