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%I #12 Apr 22 2023 11:39:01
%S 1,6,12,24,48,96,144,240,288,480,576,720,1152,1440,2880,4320,5760,
%T 8640,11520,17280,34560,51840,69120,103680,120960,172800,207360,
%U 241920,345600,362880,414720,483840,725760,967680,1209600,1451520,1935360,2419200,2903040,3628800
%N Infinitary highly totient numbers: numbers k that have more solutions x to the equation iphi(x) = k than any smaller k, where iphi is the infinitary totient function A091732.
%C Indices of records of A362485.
%C The corresponding numbers of solutions are 2, 4, 6, 10, 14, 18, 22, ... (A362488).
%H Amiram Eldar, <a href="/A362487/b362487.txt">Table of n, a(n) for n = 1..50</a>
%t solnum[n_] := Length[invIPhi[n]]; seq[kmax_] := Module[{s = {}, solmax=0}, Do[sol = solnum[k]; If[sol > solmax, solmax = sol; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[10^4] (* using the function invIPhi from A362484 *)
%Y Cf. A091732, A362484, A362485, A362486, A362488.
%Y Similar sequences: A097942, A100827, A361968, A362183.
%K nonn
%O 1,2
%A _Amiram Eldar_, Apr 22 2023