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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
Setwise difference A328246 \ A328244.
Sequence in context: A204373 A111502 A080933 * A020293 A226698 A096278
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 11 2019
STATUS
approved

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Last modified July 17 20:28 EDT 2024. Contains 374377 sequences. (Running on oeis4.)