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%I #5 Aug 03 2019 21:47:36
%S 0,0,0,0,0,0,0,7,7,14,20,34,47,73,98,136,178,241,305,402,500,636,782,
%T 974,1179,1447,1732,2093,2482,2962,3476,4107,4783,5590,6464,7494,8600,
%U 9901,11294,12907,14645,16636,18773,21214,23826,26781,29952,33517,37326
%N Number of squarefree parts in the partitions of n into 7 parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F 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(i)^2 + mu(j)^2 + mu(k)^2 + mu(l)^2 + mu(m)^2 + mu(o)^2 + mu(n-i-j-k-l-m-o)^2), where mu is the Möbius function (A008683).
%t Table[Sum[Sum[Sum[Sum[Sum[Sum[(MoebiusMu[i]^2 + MoebiusMu[j]^2 + MoebiusMu[k]^2 + MoebiusMu[l]^2 + MoebiusMu[m]^2 + MoebiusMu[o]^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 Cf. A008683.
%K nonn
%O 0,8
%A _Wesley Ivan Hurt_, Aug 03 2019
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