A328247 Numbers whose third arithmetic derivative (A099306) is a squarefree number (A005117), but the second derivative (A068346) is not.

33, 49, 98, 129, 141, 194, 205, 249, 301, 306, 445, 481, 493, 529, 549, 553, 589, 615, 681, 741, 746, 913, 917, 946, 949, 962, 973, 993, 1010, 1106, 1273, 1386, 1397, 1417, 1430, 1518, 1561, 1611, 1633, 1761, 1802, 1842, 1849, 1858, 1870, 1946, 1957, 1977, 2030, 2049, 2078, 2105, 2139, 2166, 2170, 2173, 2175, 2209, 2223, 2330

Offset

1,1

Links

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

Example

For n=33, its first arithmetic derivative is A003415(33) = 14, its second derivative is A003415(14) = 9 = 3^2 (which is not squarefree) and its third derivative is A003415(9) = 6 = 2*3, which is, thus 33 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]));
isA328247(n) = { my(u=A003415(A003415(n))); (!issquarefree(u) && issquarefree(A003415(u))); };

Crossrefs

Cf. A003415, A005117, A008966, A068346, A099306, A328234, A328244, A328245.

Setwise difference A328246 \ A328244.

Sequence in context: A204373 A111502 A080933 * A020293 A226698 A096278

Adjacent sequences: A328244 A328245 A328246 * A328248 A328249 A328250

Keyword

nonn

Author

Antti Karttunen, Oct 11 2019

Status

approved