

A328304


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


4



4, 12, 20, 28, 36, 44, 50, 52, 60, 68, 76, 84, 92, 99, 100, 116, 124, 132, 140, 148, 156, 164, 172, 180, 188, 196, 204, 207, 212, 220, 225, 228, 236, 244, 252, 260, 268, 275, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000


EXAMPLE

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.
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.


PROG

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
isA067259(n) = (2==A051903(n));
isA328303(n) = !issquarefree(A003415(n));
isA328304(n) = (isA067259(n)&&isA328303(n));


CROSSREFS

Cf. A003415, A008966, A051903.
Intersection of A067259 and A328303. Intersection of A067259 and A328321.
Cf. A328305 (a subsequence).
Sequence in context: A141065 A190748 A273253 * A031065 A017113 A316489
Adjacent sequences: A328301 A328302 A328303 * A328305 A328306 A328307


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 13 2019


STATUS

approved



