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%I #9 Jan 07 2022 11:09:53
%S 0,0,0,0,0,0,0,7,8,18,26,51,76,127,178,262,363,524,687,962,1249,1670,
%T 2136,2791,3499,4501,5569,7019,8608,10680,12915,15823,18992,22937,
%U 27279,32640,38466,45618,53378,62714,72950,85086,98275,113915,130889,150703
%N Sum of the squarefree parts of the partitions of n into 7 parts.
%H David A. Corneth, <a href="/A309482/b309482.txt">Table of n, a(n) for n = 0..9999</a>
%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)} (i * mu(i)^2 + j * mu(j)^2 + k * mu(k)^2 + l * mu(l)^2 + m * mu(m)^2 + o * mu(o)^2 + (n-i-j-k-l-m-o) * mu(n-i-j-k-l-m-o)^2), where mu is the Möbius function (A008683).
%t Table[Sum[Sum[Sum[Sum[Sum[Sum[(i * MoebiusMu[i]^2 + j * MoebiusMu[j]^2 + k * MoebiusMu[k]^2 + l * MoebiusMu[l]^2 + m * MoebiusMu[m]^2 + o * MoebiusMu[o]^2 + (n - i - j - k - l - m - o) * 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, A309459, A309478, A309479, A309480, A309481, A309482, A309484, A309485, A309486.
%K nonn
%O 0,8
%A _Wesley Ivan Hurt_, Aug 04 2019
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