A328303 Numbers whose arithmetic derivative is not squarefree.

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

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