|
%I #7 Oct 11 2019 16:56:31
%S 33,49,98,129,141,194,205,249,301,306,445,481,493,529,549,553,589,615,
%T 681,741,746,913,917,946,949,962,973,993,1010,1106,1273,1386,1397,
%U 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
%N Numbers whose third arithmetic derivative (A099306) is a squarefree number (A005117), but the second derivative (A068346) is not.
%H Antti Karttunen, <a href="/A328247/b328247.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%o (PARI)
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o isA328247(n) = { my(u=A003415(A003415(n))); (!issquarefree(u) && issquarefree(A003415(u))); };
%Y Cf. A003415, A005117, A008966, A068346, A099306, A328234, A328244, A328245.
%Y Setwise difference A328246 \ A328244.
%K nonn
%O 1,1
%A _Antti Karttunen_, Oct 11 2019
|
