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%I #32 Feb 03 2024 09:54:27
%S 18,20,28,40,44,45,50,52,54,56,63,68,75,76,80,84,88,90,92,98,99,100,
%T 104,108,112,116,117,124,126,132,135,136,140,147,148,150,152,153,156,
%U 160,162,164,168,171,172,175,176,184,188,189,196,198,200,204,207,208,212
%N Numbers k that are not squarefree, not prime powers, and not products of primorials.
%C Proper subset of A369361.
%C Superset of A368089.
%H Michael De Vlieger, <a href="/A367268/b367268.txt">Table of n, a(n) for n = 1..10000</a>
%F {a(n)} = A126706 \ A025487.
%e Let P(n) = A002110(n).
%e 12 = 6 * 2 = P(2) * P(1) is not in this sequence.
%e a(1) = 18 = 6 * 3 is not a product of primorials.
%e a(2) = 20 = 2 * 2 * 5 is not a product of primorials, etc.
%t Select[Select[Range[5000], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], Nand[EvenQ[#1], Union@ Differences@ PrimePi[#2[[All, 1]]] == {1}, AllTrue[Differences@ #2[[All, -1]], # <= 0 &]] & @@ {#, FactorInteger[#]} &]
%Y Cf. A000961, A002110, A005117, A013929, A024619, A025487, A126706, A368089, A369361.
%K nonn
%O 1,1
%A _Michael De Vlieger_, Jan 28 2024
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