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 A308954 #9 Mar 17 2025 04:10:55
%S A308954 0,0,0,0,0,0,0,1,1,2,2,4,5,8,10,13,15,22,25,33,37,49,55,71,77,98,109,
%T A308954 136,148,182,199,243,264,314,344,413,441,522,567,663,711,829,896,1036,
%U A308954 1106,1269,1370,1572,1666,1903,2041,2316,2460,2780,2971,3350,3546
%N A308954 Sum of the smallest parts in the partitions of n into 7 squarefree parts.
%H A308954 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308954 a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} mu(o)^2 * mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l-m-o)^2 * o, where mu is the Möbius function (A008683).
%F A308954 a(n) = A308953(n) - A308955(n) - A308956(n) - A308957(n) - A308958(n) - A308959(n) - A308960(n).
%t A308954 Table[Sum[Sum[Sum[Sum[Sum[Sum[o * MoebiusMu[o]^2 * MoebiusMu[m]^2 * MoebiusMu[l]^2 * MoebiusMu[k]^2 * MoebiusMu[j]^2 * MoebiusMu[i]^2 * MoebiusMu[n - i - j - k - l - m - o]^2, {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]
%Y A308954 Cf. A008683, A308952, A308953, A308955, A308956, A308957, A308958, A308959, A308960.
%K A308954 nonn
%O A308954 0,10
%A A308954 _Wesley Ivan Hurt_, Jul 03 2019