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 A308841 #10 Sep 16 2019 21:31:59
%S A308841 0,0,0,0,0,1,1,2,2,4,6,8,8,12,14,20,19,26,30,39,39,52,57,71,72,95,100,
%T A308841 123,125,155,166,198,200,242,256,304,306,366,383,445,453,533,556,642,
%U A308841 652,762,786,898,914,1048,1091,1236,1261,1434,1487,1671,1695,1919
%N A308841 Sum of the smallest parts in the partitions of n into 5 squarefree parts.
%H A308841 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308841 a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l)^2 * l, where mu is the Möbius function (A008683).
%F A308841 a(n) = A308839(n) - A308842(n) - A308843(n) - A308844(n) - A308845(n).
%e A308841 The partitions of n into 5 parts for n = 10, 11, ..
%e A308841 1+1+1+1+10
%e A308841 1+1+1+2+9
%e A308841 1+1+1+3+8
%e A308841 1+1+1+4+7
%e A308841 1+1+1+5+6
%e A308841 1+1+1+1+9 1+1+2+2+8
%e A308841 1+1+1+2+8 1+1+2+3+7
%e A308841 1+1+1+3+7 1+1+2+4+6
%e A308841 1+1+1+4+6 1+1+2+5+5
%e A308841 1+1+1+5+5 1+1+3+3+6
%e A308841 1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
%e A308841 1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
%e A308841 1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
%e A308841 1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
%e A308841 1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
%e A308841 1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
%e A308841 1+1+1+1+6 1+1+1+4+4 1+1+2+4+4 1+2+2+3+5 1+2+3+4+4
%e A308841 1+1+1+2+5 1+1+2+2+5 1+1+3+3+4 1+2+2+4+4 1+3+3+3+4
%e A308841 1+1+1+3+4 1+1+2+3+4 1+2+2+2+5 1+2+3+3+4 2+2+2+2+6
%e A308841 1+1+2+2+4 1+1+3+3+3 1+2+2+3+4 1+3+3+3+3 2+2+2+3+5
%e A308841 1+1+2+3+3 1+2+2+2+4 1+2+3+3+3 2+2+2+2+5 2+2+2+4+4
%e A308841 1+2+2+2+3 1+2+2+3+3 2+2+2+2+4 2+2+2+3+4 2+2+3+3+4
%e A308841 2+2+2+2+2 2+2+2+2+3 2+2+2+3+3 2+2+3+3+3 2+3+3+3+3
%e A308841 --------------------------------------------------------------------------
%e A308841 n | 10 11 12 13 14 ...
%e A308841 --------------------------------------------------------------------------
%e A308841 a(n) | 6 8 8 12 14 ...
%e A308841 --------------------------------------------------------------------------
%e A308841 - _Wesley Ivan Hurt_, Sep 16 2019
%t A308841 Table[Sum[Sum[Sum[Sum[l * MoebiusMu[l]^2*MoebiusMu[k]^2*MoebiusMu[j]^2* MoebiusMu[i]^2*MoebiusMu[n - i - j - k - l]^2, {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 50}]
%Y A308841 Cf. A008683, A308839, A308840, A308842, A308843, A308844, A308845.
%K A308841 nonn
%O A308841 0,8
%A A308841 _Wesley Ivan Hurt_, Jun 28 2019