A278100 Number of squarefree positive integers less than n^2.

0, 3, 6, 11, 16, 23, 31, 39, 50, 61, 75, 89, 103, 120, 139, 157, 177, 199, 219, 243, 269, 297, 323, 351, 381, 412, 444, 477, 513, 547, 584, 624, 660, 703, 745, 789, 835, 882, 928, 977, 1025, 1073, 1124, 1174, 1230, 1285, 1342, 1400, 1460, 1523, 1582, 1645, 1708

Offset: 1

Author

Jason Kimberley, Nov 12 2016

Keywords

• nonn
• easy

Links

• Jason Kimberley, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A005117, A013928, A059956.

This is the row length sequence of A277648 and A278101.

Programs

Magma

A278100:=func;
[A278100(n):n in[1..53]]; // in cubic time

Mathematica

Table[Count[Range[n^2], k_ /; SquareFreeQ@ k], {n, 53}] (* Michael De Vlieger, Nov 24 2016 *)
Module[{nn=60,sf},sf=Accumulate[Table[If[SquareFreeQ[n],1,0],{n,0,nn^2}]];Table[sf[[k^2]],{k,nn}]] (* Harvey P. Dale, Nov 14 2020 *)

PARI

a(n) = #select(x->issquarefree(x), vector(n^2-1, k, k)); \\ Michel Marcus, Nov 12 2016

Formula

a(n) = A013928(n^2).

a(n) ~ 6*n^2/Pi^2 + O(n). - Amiram Eldar, Mar 09 2021