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

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

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