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A360719 a(n) is the largest k < A126706(n) such that rad(k) = rad(A126706(n)), where rad(n) = A007947(n).

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%I A360719 #16 May 19 2023 04:24:32
%S A360719 6,12,10,18,14,24,20,22,15,36,40,26,48,28,30,21,34,54,45,38,50,42,44,
%T A360719 60,46,72,56,33,80,52,96,98,58,39,90,62,84,66,75,68,70,108,63,74,120,
%U A360719 76,51,78,100,144,82,126,57,86,35,88,150,92,94,147,162,112,132,160,102,69,104,106,192,110,196,135
%N A360719 a(n) is the largest k < A126706(n) such that rad(k) = rad(A126706(n)), where rad(n) = A007947(n).
%C A360719 Permutation of A024619.
%C A360719 Let m = A126706(n) and let R_m be the sequence of numbers k such that rad(k) = rad(m). a(n) gives the predecessor of m in R_m.
%H A360719 Michael De Vlieger, <a href="/A360719/b360719.txt">Table of n, a(n) for n = 1..10000</a>
%H A360719 Michael De Vlieger, <a href="/A360719/a360719.png">Log log scatterplot of a(n)</a>, n = 1..2^16.
%H A360719 Michael De Vlieger, <a href="/A360719/a360719_1.png">Log log scatterplot of a(n)</a>, n = 1..2^12, showing squarefree numbers in green and highlighting numbers k in A286708 with large light blue dots.
%e A360719 A126706(1) = 12; the smallest k < 12 such that rad(k) = rad(12) = 6 is a(1) = 6.
%e A360719 A126706(2) = 18; the smallest k < 18 such that rad(k) = rad(18) = 6 is a(2) = 12.
%e A360719 A126706(3) = 20; the smallest k < 20 such that rad(k) = rad(20) = 10 is a(3) = 10.
%t A360719 rad[x_] := Times@ FactorInteger[x][[All, 1]]; Table[Function[r, SelectFirst[Range[m - 1, 1, -1], rad[#] == r &]][rad[m]], {m, Select[Range[225], Nor[SquareFreeQ[#], PrimePowerQ[#]] &]}]
%Y A360719 Cf. A007947, A126706, A360529.
%K A360719 nonn
%O A360719 1,1
%A A360719 _Michael De Vlieger_, May 01 2023