A378085 First differences of A070321 (greatest squarefree number <= n).

1, 1, 0, 2, 1, 1, 0, 0, 3, 1, 0, 2, 1, 1, 0, 2, 0, 2, 0, 2, 1, 1, 0, 0, 3, 0, 0, 3, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 0, 3, 1, 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 1, 0, 0, 3, 1, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 3, 1, 1, 0, 0, 3, 1, 0, 2, 1, 1, 0

Offset: 1

Author

Gus Wiseman, Dec 04 2024

Keywords

• nonn

Examples

			The greatest squarefree number <= 50 is 47, and the greatest squarefree number <= 51 is 51, so a(51) = 4.
		

Crossrefs

Ones are A007674.

Zeros are A013929 - 1.

Twos are A280892.

Positions of first appearances are A020755 - 1 (except first term).

First-differences of A070321.

The nonsquarefree restriction is A378034, differences of A378032.

For nonsquarefree numbers we have A378036, differences of A378033.

The opposite restriction to primes is A378037, differences of A112926.

The restriction to primes is A378038, differences of A112925.

The nonsquarefree opposite is A378039, restriction A377784.

The opposite version is A378087.

A005117 lists the squarefree numbers.

A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.

Cf. A013928, A020754, A045882, A053797, A053806, A067535, A068781, A072284, A073247, A073248, A120327.

Programs

Mathematica

Differences[Table[NestWhile[#-1&,n,#>1&&!SquareFreeQ[#]&],{n,100}]]