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%I #7 Jun 29 2019 23:03:25
%S 0,0,0,0,0,0,1,2,5,5,13,19,34,38,55,74,110,125,173,206,292,333,433,
%T 493,662,729,929,1034,1323,1441,1770,1955,2403,2598,3096,3376,4066,
%U 4360,5121,5566,6584,7064,8183,8832,10326,11021,12626,13592,15701,16743,18957
%N Sum of the largest parts in the partitions of n into 6 squarefree parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(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 * (n-i-j-k-l-m), where mu is the Möbius function (A008683).
%F a(n) = A308903(n) - A308906(n) - A308907(n) - A308908(n) - A308909(n) - A308910(n).
%t Table[Sum[Sum[Sum[Sum[Sum[(n - i - j - k - l - m)*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 Cf. A008683, A308902, A308903, A308906, A308907, A308908, A308909, A308910.
%K nonn
%O 0,8
%A _Wesley Ivan Hurt_, Jun 29 2019
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