A328304 - OEIS

%I #9 Oct 13 2019 18:09:52

%S 4,12,20,28,36,44,50,52,60,68,76,84,92,99,100,116,124,132,140,148,156,

%T 164,172,180,188,196,204,207,212,220,225,228,236,244,252,260,268,275,

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

%C Numbers n for which A051903(n) = 2 and A051903(A003415(n)) > 1.

%H Antti Karttunen, <a href="/A328304/b328304.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 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 (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));

%o isA067259(n) = (2==A051903(n));

%o isA328303(n) = !issquarefree(A003415(n));

%o isA328304(n) = (isA067259(n)&&isA328303(n));

%Y Cf. A003415, A008966, A051903.

%Y Intersection of A067259 and A328303. Intersection of A067259 and A328321.

%Y Cf. A328305 (a subsequence).

%K nonn

%O 1,1

%A _Antti Karttunen_, Oct 13 2019