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%I #14 Mar 04 2023 02:08:55
%S 12,20,28,40,44,45,52,56,60,63,68,76,84,88,92,99,104,116,117,124,132,
%T 136,140,148,152,153,156,164,171,172,175,176,184,188,204,207,208,212,
%U 220,228,232,236,244,248,260,261,268,272,275,276,279,280,284,292,296,297,304,308,315,316,325,328,332,333
%N Numbers k that are neither prime power nor squarefree, such that k/rad(k) < q, where rad(k) = A007947(k) and prime q = A119288(k).
%C Proper subsequence of A126706.
%C Numbers k such that there does not exist j such that 1 < j < k and rad(j) = rad(k), but j does not divide k.
%H Michael De Vlieger, <a href="/A360767/b360767.txt">Table of n, a(n) for n = 1..10000</a>
%F This sequence is { k in A126706 : k/A007947(k) < A119288(k) } = A126706 \ A360768.
%e a(1) = 12, since 12/6 < 3.
%e a(2) = 20, since 20/10 < 5.
%e a(3) = 28, since 28/14 < 7.
%e a(4) = 40, since 40/10 < 5, etc.
%t Select[Select[Range[120], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], #1/#2 < #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@ {#, FactorInteger[#][[All, 1]]} &]
%o (PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
%o f(n) = if (isprimepower(n) || (n==1), 1, my(f=factor(n)[, 1]); f[2]); \\ A119288
%o isok(k) = !isprimepower(k) && !issquarefree(k) && (k/rad(k) < f(k)); \\ _Michel Marcus_, Mar 01 2023
%Y Cf. A007947, A013929, A024619, A119288, A126706, A355432, A360768.
%K nonn,easy
%O 1,1
%A _Michael De Vlieger_, Feb 28 2023
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