A378369 Distance between n and the least nonsquarefree number >= n.

3, 2, 1, 0, 3, 2, 1, 0, 0, 2, 1, 0, 3, 2, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 0, 1, 0, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 2, 1, 0, 0, 3, 2, 1, 0, 3, 2, 1, 0, 2, 1, 0, 0, 3, 2, 1, 0, 0, 2, 1, 0, 3, 2, 1

Offset: 1

Author

Gus Wiseman, Dec 01 2024

Keywords

• nonn

Comments

All terms are 0, 1, 2, or 3 (cf. A078147).

Crossrefs

Adding n to each term a(n) gives A120327.

Positions of 0 are A013929.

Positions of 1 are A373415.

Positions of 2 are A378458.

Positions of 3 are A007675.

Sequences obtained by adding n to each term are placed in parentheses below.

The version for primes is A007920 (A007918).

The version for perfect powers is A074984 (A377468).

The version for squarefree numbers is A081221 (A067535).

The version for non-perfect powers is A378357 (A378358).

The version for prime powers is A378370 (A000015).

The version for non prime powers is A378371 (A378372).

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

A120992 gives run-lengths of squarefree numbers increasing by one.

Cf. A073247, A151800, A236575, A243348, A375707, A377046, A378033, A378039, A378086, A378373.

Programs

Mathematica

Table[NestWhile[#+1&,n,SquareFreeQ[#]&]-n,{n,100}]