

A328247


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


3



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
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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



