cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A111732 #20 Feb 16 2025 08:32:58
%S A111732 0,16,80,161,305,561,885,1285,1861,2486,3215,3999,5023,6319,7919,9855,
%T A111732 11880,14184,16585,19085,21789,24705,27841,31441,35410,39506,44130,
%U A111732 49314,54939,60715,67115,73676,80732,88476,96576,105040,114256,123860
%N A111732 Sum of the squares of the first n nonsquarefree numbers (A013929).
%H A111732 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>.
%F A111732 a(n) = Sum_{k=1..n} A013929(k)^2.
%F A111732 a(n) ~ c * n^3, where c = Pi^4/(3*(Pi^2-6)^2) = 2.168428... . - _Amiram Eldar_, Jan 19 2024
%e A111732 a(10) = 4^2 + 8^2 + 9^2 + 12^2 + 16^2 + 18^2 + 20^2 + 24^2 + 25^2 + 27^2 = 3215.
%t A111732 Accumulate[Select[Range[0, 100], ! SquareFreeQ[#] &]^2] (* _Amiram Eldar_, Jan 19 2024 *)
%Y A111732 Cf. A000330, A005117, A013929, A111715.
%K A111732 easy,nonn
%O A111732 0,2
%A A111732 _Jonathan Vos Post_, Nov 18 2005