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 A308903 #10 Mar 11 2025 09:23:28
%S A308903 0,0,0,0,0,0,6,7,16,18,40,55,96,104,154,195,288,323,450,513,720,819,
%T A308903 1056,1196,1584,1750,2210,2457,3108,3393,4170,4588,5632,6105,7276,
%U A308903 7945,9576,10286,12084,13104,15480,16605,19278,20726,24200,25830,29624,31772
%N A308903 Sum of all the parts in the partitions of n into 6 squarefree parts.
%H A308903 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308903 a(n) = n * Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-k-j-l-m)^2, where mu is the Möbius function (A008683).
%F A308903 a(n) = n * A308902(n).
%F A308903 a(n) = A308906(n) + A308907(n) + A308908(n) + A308909(n) + A308910(n) + A308911(n).
%t A308903 Table[n*Sum[Sum[Sum[Sum[Sum[MoebiusMu[i]^2*MoebiusMu[j]^2*MoebiusMu[k]^2* MoebiusMu[l]^2*MoebiusMu[m]^2*MoebiusMu[n - i - j - k - l - m]^2, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
%Y A308903 Cf. A008683, A308902, A308906, A308907, A308908, A308909, A308910, A308911.
%K A308903 nonn
%O A308903 0,7
%A A308903 _Wesley Ivan Hurt_, Jun 29 2019