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.

A280320 Sum of the squares of the smaller parts of the partitions of 2n into two squarefree parts.

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%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