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Sum of the squares of the first n nonsquarefree numbers (A013929).
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%I #19 Jan 19 2024 04:56:37

%S 0,16,80,161,305,561,885,1285,1861,2486,3215,3999,5023,6319,7919,9855,

%T 11880,14184,16585,19085,21789,24705,27841,31441,35410,39506,44130,

%U 49314,54939,60715,67115,73676,80732,88476,96576,105040,114256,123860

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>.

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

%F a(n) ~ c * n^3, where c = Pi^4/(3*(Pi^2-6)^2) = 2.168428... . - _Amiram Eldar_, Jan 19 2024

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

%t Accumulate[Select[Range[0, 100], ! SquareFreeQ[#] &]^2] (* _Amiram Eldar_, Jan 19 2024 *)

%Y Cf. A000330, A005117, A013929, A111715.

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Nov 18 2005