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

1,1

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