A328245 Numbers whose second arithmetic derivative (A068346) is a squarefree number (A005117), but the first derivative (A003415) is not.

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

Offset: 1

Author

Antti Karttunen, Oct 11 2019

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A003415, A005117, A008966, A068346.

Setwise difference A328244 \ A328234.

Cf. A328253 (a subsequence, nonsquarefree terms).

Programs

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.