OFFSET
1,2
COMMENTS
These are points at which the second differences (A376593) are nonzero.
LINKS
EXAMPLE
The nonsquarefree numbers (A013929) are:
4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, 52, 54, ...
with first differences (A078147):
4, 1, 3, 4, 2, 2, 4, 1, 2, 1, 4, 4, 4, 4, 1, 3, 1, 1, 2, 2, 2, 4, 3, 1, 4, 4, 3, ...
with first differences (A376593):
-3, 2, 1, -2, 0, 2, -3, 1, -1, 3, 0, 0, 0, -3, 2, -2, 0, 1, 0, 0, 2, -1, -2, 3, ...
with nonzeros (A376594) at:
1, 2, 3, 4, 6, 7, 8, 9, 10, 14, 15, 16, 18, 21, 22, 23, 24, 26, 27, 28, 29, 30, ...
MATHEMATICA
Join@@Position[Sign[Differences[Select[Range[100], !SquareFreeQ[#]&], 2]], 1|-1]
CROSSREFS
The first differences were A078147.
These are the nonzeros of A376593.
The complement is A376594.
A114374 counts integer partitions into nonsquarefree numbers.
For points of nonzero curvature: A333214 (prime), A376603 (composite), A376589 (non-perfect-power), A376592 (squarefree), A376598 (prime-power), A376601 (non-prime-power).
For nonsquarefree numbers: A078147 (first differences), A376593 (second differences), A376594 (inflections and undulations).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 04 2024
STATUS
approved