A378039 a(1)=3; a(n>1) = n-th first difference of A120327(k) = least nonsquarefree number greater than k.

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

Offset: 1

Author

Gus Wiseman, Nov 18 2024

Keywords

• nonn

Comments

The union is {0,1,2,3,4}.

Crossrefs

Positions of 0's are A005117.

Positions of 4's are A007675 - 1, except first term.

Positions of 1's are A068781.

Positions of 2's are A073247 - 1.

Positions of 3's are A073248 - 1, except first term.

First-differences of A120327.

For prime-powers we have A377780, first-differences of A000015.

Restriction is A377784 (first-differences of A377783, union A378040).

The opposite is A378036 (differences A378033), for prime-powers A377782.

The opposite for squarefree is A378085, differences of A070321

For squarefree we have A378087, restriction A378037, differences of A112926.

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers.

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

A061398 counts squarefree numbers between primes, zeros A068360.

A061399 counts nonsquarefree numbers between primes, zeros A068361.

Cf. A013928, A053797, A053806, A072284, A224363, A377047, A377049, A378032, A378034, A378082, A378083, A378084.

Programs

Mathematica

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