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%I #12 Apr 10 2023 05:14:29
%S 1,6,8,12,24,48,96,120,144,240,480,576,720,1440,2880,4320,5760,8640,
%T 10080,17280,20160,30240,34560,40320,60480,80640,120960,241920,362880,
%U 483840,725760,967680,1209600,1451520,2177280,2419200,2903040,3628800,4354560,4838400
%N 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).
%C Indices of records of A361967.
%C The corresponding numbers of solutions are 2, 3, 4, 5, 8, 11, ... (A361971).
%H Amiram Eldar, <a href="/A361968/b361968.txt">Table of n, a(n) for n = 1..51</a>
%t 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 *)
%Y The unitary version of A097942.
%Y Cf. A047994, A135347, A347771, A361966, A361967, A361969, A361970, A361971.
%K nonn
%O 1,2
%A _Amiram Eldar_, Apr 01 2023