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

1,4

Links

Table of n, a(n) for n=1..87.

Example

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

Mathematica

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

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.

Sequence in context: A212551 A125753 A185184 * A292894 A147701 A228348

Adjacent sequences: A378082 A378083 A378084 * A378086 A378087 A378088

Keyword

nonn

Author

Gus Wiseman, Dec 04 2024

Status

approved