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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

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Last modified November 22 00:32 EST 2019. Contains 329383 sequences. (Running on oeis4.)