

A328303


Numbers whose arithmetic derivative is not squarefree.


6



0, 1, 4, 8, 12, 14, 15, 16, 20, 24, 27, 28, 32, 35, 36, 39, 40, 44, 46, 48, 50, 51, 52, 54, 55, 56, 60, 64, 65, 68, 72, 76, 77, 80, 81, 84, 86, 87, 88, 91, 92, 94, 95, 96, 99, 100, 104, 108, 111, 112, 115, 116, 119, 120, 122, 123, 124, 125, 128, 132, 135, 136, 138, 140, 141, 143, 144, 146, 148, 152, 155, 156, 158, 159, 160, 162, 164, 168, 172, 176, 180, 183, 184, 187, 188, 189, 192, 194, 196, 200
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OFFSET

1,3


COMMENTS

Numbers n for which either A003415(n) = 0 or A051903(A003415(n)) > 1.


LINKS

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


EXAMPLE

Arithmetic derivative of 1 is A003415(1) = 0, which is not a squarefree number (not in A005117), thus 1 is included in this sequence. Ditto for 0, as A003415(0) = 0.
Arithmetic derivative of 8 is A003415(8) = 12 = 2^2 * 3, which is not squarefree, thus 8 is included in this sequence.
Arithmetic derivative of 15 is A003415(15) = 8 = 2^3, which is not squarefree, thus 15 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]));
isA328303(n) = !issquarefree(A003415(n));


CROSSREFS

Cf. A003415, A005177, A008966, A051903.
Complement of the union of A000040 and A328234.
Cf. A328245, A328251, A328253, A328304, A328305 (subsequences).
Sequence in context: A101887 A320498 A311078 * A311079 A257221 A092453
Adjacent sequences: A328300 A328301 A328302 * A328304 A328305 A328306


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 13 2019


STATUS

approved



