A378036 First differences of A378033 (greatest positive integer < n that is 1 or nonsquarefree).

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

Offset: 1

Author

Gus Wiseman, Nov 18 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65539

Crossrefs

Positions of 0 are A005117 - 1, complement A013929 - 1.

Sums for squarefree numbers are A070321 (restriction A112925).

The restricted opposite is A377784, differences of A377783 (union A378040).

First-differences of A378033.

The restriction is A378034, differences of A378032.

The restricted opposite for squarefree is A378037, differences of A112926.

The opposite is A378039, differences of A120327 (union A162966).

For squarefree numbers we have A378085, restriction A378038.

The opposite for squarefree is A378087, differences of A067535.

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers, differences A076259, seconds A376590.

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

A061398 counts squarefree numbers between primes (sums A337030), zeros A068360.

A061399 counts nonsquarefree numbers between primes (sums A378086), zeros A068361.

A377046 encodes k-differences of nonsquarefree numbers, zeros A377050.

Cf. A053797, A053806, A065514, A377047, A377048, A377049, A377703, A378082, A378083, A378084.

Programs

Mathematica

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

PARI

A378033(n) = if(n<=3, 1, forstep(k=n, 0, -1, if(!issquarefree(k), return(k))));
A378036(n) = (A378033(1+n)-A378033(n)); \\ Antti Karttunen, Jan 28 2025

Formula

a(prime(n)) = A378034(n).

Extensions

Data section extended to a(107) by Antti Karttunen, Jan 28 2025