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A328304 Numbers that are cubefree, but not squarefree and whose arithmetic derivative is not squarefree.

%I A328304 #9 Oct 13 2019 18:09:52
%S A328304 4,12,20,28,36,44,50,52,60,68,76,84,92,99,100,116,124,132,140,148,156,
%T A328304 164,172,180,188,196,204,207,212,220,225,228,236,244,252,260,268,275,
%U A328304 276,284,292,300,306,308,316,332,340,348,356,364,372,380,388,396,404,412,420,428,436,441,444,452,460,468,476,484,492,508,516,524,525
%N A328304 Numbers that are cubefree, but not squarefree and whose arithmetic derivative is not squarefree.
%C A328304 Numbers n for which A051903(n) = 2 and A051903(A003415(n)) > 1.
%H A328304 Antti Karttunen, <a href="/A328304/b328304.txt">Table of n, a(n) for n = 1..10000</a>
%e A328304 4 = 2^2 is cubefree but not squarefree, and its arithmetic derivative A003415(4) = 4 is not squarefree, thus 4 is included in this sequence.
%e A328304 225 = 3^2 * 5^2 is cubefree but not squarefree, and its arithmetic derivative A003415(225) = 240 = 2^4 * 3 * 5 is not squarefree, thus 225 is included in this sequence.
%o A328304 (PARI)
%o A328304 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328304 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
%o A328304 isA067259(n) = (2==A051903(n));
%o A328304 isA328303(n) = !issquarefree(A003415(n));
%o A328304 isA328304(n) = (isA067259(n)&&isA328303(n));
%Y A328304 Cf. A003415, A008966, A051903.
%Y A328304 Intersection of A067259 and A328303. Intersection of A067259 and A328321.
%Y A328304 Cf. A328305 (a subsequence).
%K A328304 nonn
%O A328304 1,1
%A A328304 _Antti Karttunen_, Oct 13 2019