A328246 Numbers whose third arithmetic derivative (A099306) is a squarefree number (A005117).

9, 14, 18, 21, 25, 33, 38, 46, 49, 57, 65, 77, 85, 93, 98, 121, 126, 129, 134, 138, 141, 145, 150, 161, 166, 177, 185, 186, 194, 201, 205, 206, 209, 217, 221, 237, 242, 249, 253, 258, 262, 265, 266, 289, 290, 301, 305, 306, 315, 322, 326, 333, 334, 338, 341, 342, 350, 361, 365, 369, 375, 377, 381, 393, 398, 402, 413, 414

Offset

1,1

Comments

Numbers n for which A008966(A003415(A003415(A003415(n)))) = 1.

Links

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

Example

For n=9, its first arithmetic derivative is A003415(9) = 6, its second derivative is A003415(6) = 5, and its third derivative is A003415(5) = 1, and 1 is a squarefree number (in A005117), thus 9 is included in this sequence.
For n=14, A003415(14) = 9, A003415(9) = 6, A003415(6) = 5, and 5, like all primes, is a squarefree number, thus 14 is included in this sequence.
For n=49, A003415(49) = 14, A003415(14) = 9, A003415(9) = 6 = 2*3, and 6 is a squarefree number, thus 49 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]));
isA328246(n) = { my(u=A003415(A003415(A003415(n)))); (u>0 && issquarefree(u)); };

Crossrefs

Cf. A003415, A005117, A008966, A099306, A328234, A328244, A328245.

Cf. A192192, A328239, A328247 (subsequences).

Sequence in context: A011767 A305092 A205690 * A244466 A171123 A327896

Adjacent sequences: A328243 A328244 A328245 * A328247 A328248 A328249

Keyword

nonn

Author

Antti Karttunen, Oct 11 2019

Status

approved