A072906 - OEIS

A072906

Least k >=1 such that floor(n/k) is squarefree.

1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 2, 1, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 4, 4, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 7, 7, 5, 1, 2, 1, 4, 1, 4, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 2, 2, 1, 1, 1, 3, 6, 1, 1, 2, 1, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 5, 1, 5, 3, 3, 1, 1, 1, 3, 1

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OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

sum(k=1, a(k)) is asymptotic to C*n with C=1.9091.....

MATHEMATICA

Array[Block[{k = 1}, While[! SquareFreeQ@ Floor[#/k], k++]; k] &, 120] (* Michael De Vlieger, Nov 20 2017 *)

PROG

(PARI) a(n)=if(n<0, 0, s=1; while(issquarefree(floor(n/s))==0, s++); s)

CROSSREFS