A120327 Smallest nonsquarefree number >= n.

4, 4, 4, 4, 8, 8, 8, 8, 9, 12, 12, 12, 16, 16, 16, 16, 18, 18, 20, 20, 24, 24, 24, 24, 25, 27, 27, 28, 32, 32, 32, 32, 36, 36, 36, 36, 40, 40, 40, 40, 44, 44, 44, 44, 45, 48, 48, 48, 49, 50, 52, 52, 54, 54, 56, 56, 60, 60, 60, 60, 63, 63, 63, 64, 68, 68, 68, 68, 72, 72, 72, 72

Offset: 1

Author

Zak Seidov, Aug 16 2006

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

For squarefree instead of nonsquarefree we have A067535, differences A378087.

The opposite for squarefree is A070321, differences A378085.

The run-lengths are A078147 if we prepend 4, differences A376593.

The restriction to primes is A377783 (union A378040), differences A377784.

The opposite is A378033 (differences A378036), for prime powers A031218.

First differences are A378039 if we assume that a(1) = 1.

A005117 lists the squarefree numbers.

A013929 lists the nonsquarefree numbers.

A061398 counts squarefree numbers between primes, zeros A068360.

A061399 counts nonsquarefree numbers between primes, zeros A068361.

Restriction to primes: A112925, A112926, A337030, A378032, A378034, A378037, A378038, A378082, A378084.

Cf. A000015, A007675, A013928, A053797, A053806, A068781, A072284, A073247, A120992, A224363.

Programs

Mathematica

Table[NestWhile[ #+1&,n,SquareFreeQ],{n,100}] (* simplified by Harvey P. Dale, Apr 08 2014 *)