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.
%I A280320 #25 Jan 22 2023 12:05:04 %S A280320 1,5,10,14,34,66,59,75,84,220,205,309,373,600,565,665,839,1103,959, %T A280320 1191,1176,1860,1416,2060,1664,3653,2194,3505,2891,4974,3563,5534, %U A280320 4371,7551,5845,8874,6742,10409,7061,10145,8037,12414,9030,13327,10849,15319,13473,15960 %N A280320 Sum of the squares of the smaller parts of the partitions of 2n into two squarefree parts. %H A280320 Harvey P. Dale, <a href="/A280320/b280320.txt">Table of n, a(n) for n = 1..1000</a> %H A280320 <a href="/index/Par#part">Index entries for sequences related to partitions</a> %F A280320 a(n) = Sum_{i=1..n} i^2 * mu(i)^2 * mu(2n-i)^2, where mu is the Möbius function (A008683). %F A280320 a(n) = A280316(n) - A280322(n). %p A280320 with(numtheory): A280320:=n->add(i^2*mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280320(n), n=1..100); %t A280320 Table[Total[Select[IntegerPartitions[2 n,{2}],AllTrue[#,SquareFreeQ]&][[All,2]]^2],{n,50}] (* _Harvey P. Dale_, Jan 22 2023 *) %o A280320 (PARI) a(n) = sum(i=1, n, i^2*issquarefree(i)*issquarefree(2*n-i)); \\ _Michel Marcus_, May 16 2019 %Y A280320 Cf. A008683, A280226, A280316, A280322. %K A280320 nonn,easy %O A280320 1,2 %A A280320 _Wesley Ivan Hurt_, Dec 31 2016