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%I #18 Feb 07 2020 03:01:12
%S 1,6,12,24,48,72,144,288,576,864,1152,1440,1728,2160,2304,2880,4320,
%T 5760,8640,17280,25920,34560,51840,69120,103680,120960,138240,155520,
%U 181440,207360,241920,311040,362880,414720,483840,622080,725760,967680,1244160,1451520
%N Indices of records in A332042.
%C Numbers k such that psi(x) = k has more solutions x than any smaller k, where psi(x) is the Dedekind psi function (A001615).
%C The corresponding number of solutions for each term is 1, 2, 4, 5, 6, 9, 11, 17, ... (see the link for more values).
%H Amiram Eldar, <a href="/A332043/b332043.txt">Table of n, a(n) for n = 1..59</a>
%H Amiram Eldar, <a href="/A332043/a332043.txt">Table of n, a(n), A332042(a(n)) for n = 1..59</a>
%e There are 2 solutions to psi(x) = 6: psi(4) = psi(5) = 6. For all m < 6 there are no more than one solution to psi(x) = m, thus 6 is in the sequence.
%t psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); m = 10000; v = Table[0, {m}]; Do[i = psi[k]; If[i <= m, v[[i]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s
%Y Cf. A001615, A145899, A289132, A332037, A332039, A332041, A332042.
%K nonn
%O 1,2
%A _Amiram Eldar_, Feb 05 2020