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A362844 a(n) is the largest k < A360768(n) such that rad(k) = rad(A360768(n)) and n mod k != 0, where rad(n) = A007947(n).

%I A362844 #8 May 20 2023 15:05:09
%S A362844 12,18,24,36,40,48,54,45,50,60,72,56,80,96,98,90,84,75,108,63,120,100,
%T A362844 144,126,150,147,162,112,132,160,192,196,135,156,180,176,175,200,168,
%U A362844 198,240,216,252,270,204,234,250,288,294,208,228,280,242,300,297,225,336,324,224,264,320,375,306,276
%N A362844 a(n) is the largest k < A360768(n) such that rad(k) = rad(A360768(n)) and n mod k != 0, where rad(n) = A007947(n).
%C A362844 Largest nondivisor less than m = A360768(n) that shares the same squarefree kernel as m.
%C A362844 a(n) is in A126706, not a permutation of A126706.
%H A362844 Michael De Vlieger, <a href="/A362844/b362844.txt">Table of n, a(n) for n = 1..10000</a>
%H A362844 Michael De Vlieger, <a href="/A362844/a362844.png">Log log scatterplot of a(n)</a>, n = 1..2^12, showing records in red.
%e A362844 A360768(1) = 18; the smallest nondivisor k < 18 such that rad(k) = rad(18) = 6 is a(1) = 12.
%e A362844 A360768(2) = 24; the smallest nondivisor k < 24 such that rad(k) = rad(24) = 6 is a(2) = 18.
%e A362844 A360768(5) = 50; the smallest nondivisor k < 50 such that rad(k) = rad(50) = 10 is a(5) = 40.
%t A362844 rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; s = Select[Select[Range[414],  Nor[SquareFreeQ[#], PrimePowerQ[#]] &], #1/#2 >= #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@ {#, FactorInteger[#][[All, 1]]} &]; Table[Function[r, SelectFirst[Range[m - 1, 1, -1], r == rad[#] &] ][rad[m]], {m, s}]
%Y A362844 Cf. A007947, A126706, A360768, A362041.
%K A362844 nonn
%O A362844 1,1
%A A362844 _Michael De Vlieger_, May 19 2023