A376592 - OEIS

A376592

Points of nonzero curvature in the sequence of squarefree numbers (A005117).

2, 3, 5, 6, 7, 8, 10, 13, 15, 17, 19, 20, 22, 23, 25, 26, 28, 29, 30, 31, 34, 36, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 51, 52, 54, 57, 59, 60, 61, 63, 64, 66, 67, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 85, 86, 88, 89, 90, 91, 92, 93, 94, 95

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OFFSET

1,1

COMMENTS

These are points at which the second differences (A376590) are nonzero.

LINKS

Table of n, a(n) for n=1..67.

Gus Wiseman, Points of nonzero curvature in the squarefree numbers.

EXAMPLE

The squarefree numbers (A005117) are:

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, ...

with first differences (A076259):

1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, ...

with first differences (A376590):

0, 1, -1, 0, 2, -2, 1, -1, 0, 1, 0, 0, -1, 0, 2, 0, -2, 0, 1, -1, 0, 1, -1, 0, 1, ...

with nonzeros at (A376591):

2, 3, 5, 6, 7, 8, 10, 13, 15, 17, 19, 20, 22, 23, 25, 26, 28, 29, 30, 31, 34, 36, ...

MATHEMATICA

Join@@Position[Sign[Differences[Select[Range[100], SquareFreeQ], 2]], 1|-1]

CROSSREFS

The first differences were A076259, see also A375927, A376305, A376306, A376307, A376311.

These are the nonzeros of A376590.

The complement is A376591.

A000040 lists the prime numbers, differences A001223.

A005117 lists squarefree numbers, complement A013929 (differences A078147).

A073576 counts integer partitions into squarefree numbers, factorizations A050320.

For points of nonzero curvature: A333214 (prime), A376603 (composite), A376589 (non-perfect-power), A376595 (nonsquarefree), A376598 (prime-power), A376601 (non-prime-power).

For squarefree numbers: A076259 (first differences), A376590 (second differences), A376591 (inflection and undulation points).

Cf. A007674, A036263, A053797, A053806, A061398, A072284, A112925, A112926, A120992, A333254, A373198, A376655.

Sequence in context: A274779 A120486 A229993 * A323252 A219255 A025501

Adjacent sequences: A376589 A376590 A376591 * A376593 A376594 A376595

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 04 2024

STATUS

approved