

A328245


Numbers whose second arithmetic derivative (A068346) is a squarefree number (A005117), but the first derivative (A003415) is not.


7



14, 46, 50, 65, 77, 86, 94, 99, 122, 125, 138, 146, 207, 230, 302, 334, 343, 346, 375, 426, 531, 546, 554, 581, 590, 626, 662, 682, 686, 710, 717, 718, 725, 734, 747, 750, 819, 842, 869, 875, 931, 965, 1002, 1041, 1083, 1130, 1145, 1146, 1166, 1175, 1202, 1241, 1265, 1310, 1331, 1337, 1349, 1375, 1418, 1461, 1466, 1469, 1501, 1529, 1541
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OFFSET

1,1


LINKS

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


EXAMPLE

For n = 14, its first arithmetic derivative, A003415(14) = 9 = 3^2 is not squarefree, while the second arithmetic derivative, A003415(9) = 6 = 2* 3 is, thus 14 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]));
isA328245(n) = { my(u=A003415(n)); (!issquarefree(u) && issquarefree(A003415(u))); }; \\ issquarefree(0) returns 0 as zero is not considered as a squarefree number.


CROSSREFS

Cf. A003415, A005117, A008966, A068346.
Setwise difference A328244 \ A328234.
Cf. A328253 (a subsequence, nonsquarefree terms).
Sequence in context: A243384 A242579 A206208 * A039368 A043191 A043971
Adjacent sequences: A328242 A328243 A328244 * A328246 A328247 A328248


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 11 2019


STATUS

approved



