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 A308783 #8 Aug 14 2022 16:11:30
%S A308783 0,0,0,0,4,5,12,14,32,36,60,66,96,104,154,165,240,255,342,380,500,504,
%T A308783 660,690,888,900,1144,1161,1484,1508,1800,1860,2272,2277,2720,2800,
%U A308783 3348,3404,4028,4056,4880,4879,5670,5762,6820,6840,7912,8084,9312,9408
%N A308783 Sum of all the parts in the partitions of n into 4 squarefree parts.
%H A308783 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308783 a(n) = n * Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k)^2, where mu is the Möbius function (A008683).
%F A308783 a(n) = n * A308767(n).
%F A308783 a(n) = A308768(n) + A308762(n) + A308769(n) + A308770(n).
%t A308783 Table[n*Sum[Sum[Sum[MoebiusMu[k]^2*MoebiusMu[j]^2*MoebiusMu[i]^2* MoebiusMu[n - i - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 50}]
%t A308783 Table[Total[Flatten[Select[IntegerPartitions[n,{4}],AllTrue[#,SquareFreeQ]&]]],{n,0,50}] (* _Harvey P. Dale_, Aug 14 2022 *)
%Y A308783 Cf. A008683, A308767, A308762, A308768, A308769, A308770.
%K A308783 nonn
%O A308783 0,5
%A A308783 _Wesley Ivan Hurt_, Jun 24 2019