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%I #10 Apr 11 2023 04:17:58
%S 0,6,10,20,31,47,53,65,77,89,113,119,149,167,179,209,293,299,329,359,
%T 389,419,479,509,599,629,779,839,989,1049,1139,1259,1469,1559,1649,
%U 1679,1889,2099,2309,2729,3149,3359,3569,3989,4289,4409,4619,5249,5459,6089,6509
%N Unitary highly cototient numbers: numbers k that have more solutions x to the equation A323410(x) = k than any smaller k.
%C Indices of records of A362181.
%C The corresponding numbers of solutions are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 21, ... (A362184).
%H Amiram Eldar, <a href="/A362183/b362183.txt">Table of n, a(n) for n = 1..96</a> (terms below 10^5)
%t ucototient[n_] := n - Times @@ (Power @@@ FactorInteger[n] - 1); ucototient[1] = 0; With[{max = 300}, solnum = Table[0, {n, 1, max}]; Do[If[(i = ucototient[k]) <= max, solnum[[i]]++], {k, 2, max^2}]; s = {0}; solmax=1; Do[sol = solnum[[k]]; If[sol > solmax, solmax = sol; AppendTo[s, k]], {k, 2, max}]; s]
%Y Cf. A323410, A362181, A362184.
%Y The unitary version of A100827.
%Y Similar sequences: A097942, A361968.
%K nonn
%O 1,2
%A _Amiram Eldar_, Apr 10 2023
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