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

Offset

1,4

Links

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

Amiram Eldar, Plot of Sum_{k=1..n} a(k)/n for n = 2^(19..33).

Formula

Sum_{k=1..n} a(k) is asymptotic to C*n with C = 1.9091...

Apparently C = 1.908762... (see the plot in the Links section). - Amiram Eldar, Feb 03 2025

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

Cf. A005117.

Sequence in context: A185812 A152798 A079115 * A239062 A341052 A201160

Adjacent sequences: A072903 A072904 A072905 * A072907 A072908 A072909

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 10 2002

Status

approved