A111732 Sum of the squares of the first n nonsquarefree numbers (A013929).

0, 16, 80, 161, 305, 561, 885, 1285, 1861, 2486, 3215, 3999, 5023, 6319, 7919, 9855, 11880, 14184, 16585, 19085, 21789, 24705, 27841, 31441, 35410, 39506, 44130, 49314, 54939, 60715, 67115, 73676, 80732, 88476, 96576, 105040, 114256, 123860

Offset: 0

Author

Jonathan Vos Post, Nov 18 2005

Keywords

• easy
• nonn

Examples

			a(10) = 4^2 + 8^2 + 9^2 + 12^2 + 16^2 + 18^2 + 20^2 + 24^2 + 25^2 + 27^2 = 3215.
		

Links

• Eric Weisstein's World of Mathematics, Squarefree.

Crossrefs

Cf. A000330, A005117, A013929, A111715.

Programs

Mathematica

Accumulate[Select[Range[0, 100], ! SquareFreeQ[#] &]^2] (* Amiram Eldar, Jan 19 2024 *)

Formula

a(n) = Sum_{k=1..n} A013929(k)^2.

a(n) ~ c * n^3, where c = Pi^4/(3*(Pi^2-6)^2) = 2.168428... . - Amiram Eldar, Jan 19 2024