A378040 Union of A377783(n) = least nonsquarefree number > prime(n).

4, 8, 12, 16, 18, 20, 24, 32, 40, 44, 48, 54, 60, 63, 68, 72, 75, 80, 84, 90, 98, 104, 108, 112, 116, 128, 132, 140, 150, 152, 160, 164, 168, 175, 180, 184, 192, 196, 198, 200, 212, 224, 228, 232, 234, 240, 242, 252, 260, 264, 270, 272, 279, 284, 294, 308, 312

Offset: 1

Author

Gus Wiseman, Nov 20 2024

Keywords

• nonn

Comments

Numbers k such that, if p is the greatest prime < k, all numbers from p to k (exclusive) are squarefree.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

For squarefree we have A112926 (diffs A378037), opposite A112925 (diffs A378038).

For prime-power instead of nonsquarefree we have A345531, differences A377703.

Union of A377783 (diffs A377784), restriction of A120327 (diffs A378039).

Nonsquarefree numbers not appearing are A378084, see also A378082, A378083.

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.

A070321 gives the greatest squarefree number up to n.

A071403(n) = A013928(prime(n)) counts squarefree numbers up to prime(n).

A378086(n) = A057627(prime(n)) counts nonsquarefree numbers up to prime(n).

Cf. A378034 (differences of A378032), restriction of A378036 (differences A378033).

Cf. A000015, A053797, A053806, A072284, A224363, A337030, A377047, A377049, A377430, A377431.

Programs

Mathematica

Union[Table[NestWhile[#+1&,Prime[n],SquareFreeQ],{n,100}]]
lns[p_]:=Module[{k=p+1},While[SquareFreeQ[k],k++];k]; Table[lns[p],{p,Prime[Range[70]]}]//Union (* Harvey P. Dale, Jun 12 2025 *)