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%I #8 Jul 27 2019 06:23:49
%S 1,12,60,420,4620,360,1021020,19399380,446185740,13860,401120980260,
%T 2520,608500527054420,26165522663340060,180180,65178316954380089460,
%U 3845520700308425278140,234576762718813941966540,15716643102160534111758180,27720,3063060,6435289534681345815798169108260
%N Least number k with A309004(k) = n.
%F a(k) <= A088860(k).
%e a(3) = 60 since 60 is the least number with 3 numbers having the same prime signature and set of distinct prime factor as 60: 60 = 2^2 * 3 * 5, 90 = 3^2 * 2 * 5, and 150 = 5^2 * 2 * 3.
%t a[n_] := Multinomial @@ Tally[FactorInteger[n][[;;,2]]][[;;,2]]; m = 6; s = Table[0, {m}]; c = 0; n = 1; While[c < m, i = a[n]; If[i <= m && s[[i]] == 0, s[[i]] = n; c++]; n++]; s
%Y Cf. A088860, A111470, A309004.
%Y Subsequence of A025487.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jul 22 2019