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

1,2

Links

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

Formula

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

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

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 *)

Prog

(Magma)
A278100:=func<n|#[k:k in[1..n^2-1]|IsSquarefree(k)]>;
[A278100(n):n in[1..53]]; // in cubic time
(PARI) a(n) = #select(x->issquarefree(x), vector(n^2-1, k, k)); \\ Michel Marcus, Nov 12 2016

Crossrefs

Cf. A005117, A013928, A059956.

This is the row length sequence of A277648 and A278101.

Sequence in context: A266252 A267260 A116940 * A087099 A181947 A366969

Adjacent sequences: A278097 A278098 A278099 * A278101 A278102 A278103

Keyword

nonn,easy

Author

Jason Kimberley, Nov 12 2016

Status

approved