A070321 Greatest squarefree number <= n.

1, 2, 3, 3, 5, 6, 7, 7, 7, 10, 11, 11, 13, 14, 15, 15, 17, 17, 19, 19, 21, 22, 23, 23, 23, 26, 26, 26, 29, 30, 31, 31, 33, 34, 35, 35, 37, 38, 39, 39, 41, 42, 43, 43, 43, 46, 47, 47, 47, 47, 51, 51, 53, 53, 55, 55, 57, 58, 59, 59, 61, 62, 62, 62, 65, 66, 67, 67, 69, 70, 71, 71

Offset

1,2

Comments

a(n) = Max( core(k) : k=1,2,3,...,n ) where core(x) is the squarefree part of x (the smallest integer such that x*core(x) is a square).

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Maple

A070321 := proc(n)
    local a;
    for a from n by -1 do
        if issqrfree(a) then
            return a;
        end if;
    end do:
end proc:
seq(A070321(n), n=1..100) ; # R. J. Mathar, May 25 2023

Mathematica

a[n_] :=For[ k = n, True, k--, If[ SquareFreeQ[k], Return[k]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 27 2013 *)
gsfn[n_]:=Module[{k=n}, While[!SquareFreeQ[k], k--]; k]; Array[gsfn, 80] (* Harvey P. Dale, Mar 27 2013 *)

Prog

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

Crossrefs

Cf. A005117, A007947, A067535, A076260.

Cf. A081217, A081218, A081210.

Sequence in context: A081213 A081210 A285719 * A239904 A334819 A338375

Adjacent sequences: A070318 A070319 A070320 * A070322 A070323 A070324

Keyword

easy,nonn

Author

Benoit Cloitre, May 11 2002

Extensions

New description from Reinhard Zumkeller, Oct 03 2002

Status

approved