A179213 Sum of squarefree numbers between n and 2*n (inclusive).

3, 5, 14, 18, 28, 34, 55, 63, 80, 99, 132, 144, 170, 157, 202, 218, 285, 303, 378, 398, 481, 503, 527, 551, 551, 602, 629, 684, 799, 829, 922, 891, 1022, 1056, 1161, 1197, 1344, 1307, 1424, 1464, 1546, 1588, 1717, 1761, 1850, 1941, 2082, 2130, 2227, 2227

Offset: 1

Author

Reinhard Zumkeller, Jul 05 2010

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005117, A045943, A066779, A073837, A179211, A179214.

Programs

Mathematica

Table[Total[Select[Range[n,2n],SquareFreeQ]],{n,50}] (* Harvey P. Dale, Apr 29 2017 *)

Formula

a(n) = Sum_{k=n..2*n} k*A008966(k).

A073837(n) <= a(n) <= A045943(n);

a(n) = A066779(2*n) - A066779(n-1).

a(n) ~ (9/Pi^2) * n^2 + O(n^(3/2)). - Amiram Eldar, Mar 07 2021