A375712 Numbers k such that A013929(k+1) - A013929(k) = 4. In other words, the k-th nonsquarefree number is 4 less than the next nonsquarefree number.

1, 4, 7, 11, 12, 13, 14, 22, 25, 26, 29, 32, 35, 39, 40, 41, 42, 50, 53, 54, 61, 64, 70, 71, 72, 75, 78, 81, 82, 83, 84, 87, 90, 98, 99, 102, 109, 110, 117, 120, 123, 124, 127, 135, 139, 140, 144, 151, 154, 155, 156, 157, 160, 163, 168, 169, 170, 173, 176, 179

Offset

1,2

Comments

The difference of consecutive nonsquarefree numbers is at least 1 and at most 4, so there are four disjoint sequences of this type:

- A375709 (difference 1)

- A375710 (difference 2)

- A375711 (difference 3)

- A375712 (difference 4)

Links

Table of n, a(n) for n=1..60.

Formula

Complement of A375709 U A375710 U A375711.

Example

The initial nonsquarefree numbers are 4, 8, 9, 12, 16, 18, 20, 24, 25, which first increase by 4 after the first, fourth, and seventh terms.

Mathematica

Join@@Position[Differences[Select[Range[100], !SquareFreeQ[#]&]], 4]

Crossrefs

For prime numbers we have A029709.

Positions of 4's in A078147.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

A053797 gives lengths of runs of nonsquarefree numbers, firsts A373199.

A375707 counts squarefree numbers between consecutive nonsquarefree numbers.

Cf. A007674, A014689, A029707, A049094, A061399, A068781, A072284, A110969, A120992, A294242, A375927.

Sequence in context: A198468 A032547 A075630 * A274341 A164888 A023985

Adjacent sequences: A375709 A375710 A375711 * A375713 A375714 A375715

Keyword

nonn

Author

Gus Wiseman, Sep 09 2024

Status

approved