A067535 Smallest squarefree number >= n.

1, 2, 3, 5, 5, 6, 7, 10, 10, 10, 11, 13, 13, 14, 15, 17, 17, 19, 19, 21, 21, 22, 23, 26, 26, 26, 29, 29, 29, 30, 31, 33, 33, 34, 35, 37, 37, 38, 39, 41, 41, 42, 43, 46, 46, 46, 47, 51, 51, 51, 51, 53, 53, 55, 55, 57, 57, 58, 59, 61, 61, 62

Offset: 1

Author

Reinhard Zumkeller, Jan 27 2002

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Squarefree.

Crossrefs

Cf. A005117, A070321, A076260, A081221.

Programs

Maple

A067535 := proc(n)
    for a from n do
        if issqrfree(a) then
            return a ;
        end if;
    end do:
end proc:
seq(A067535(n),n=1..100) ; # R. J. Mathar, May 31 2024

Mathematica

Table[k = n; While[! SquareFreeQ@ k, k++]; k, {n, 62}] (* Michael De Vlieger, Mar 18 2017 *)

PARI

a(n) = while (! issquarefree(n), n++); n; \\ Michel Marcus, Mar 18 2017

Python

from itertools import count
from sympy import factorint
def A067535(n): return next(m for m in count(n) if max(factorint(m).values(),default=0)<=1) # Chai Wah Wu, Dec 04 2024

Formula

a(n) = n + A081221(n). - Amiram Eldar, Oct 10 2023