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%I A308906 #7 Jun 29 2019 23:02:51
%S A308906 0,0,0,0,0,0,1,1,2,2,4,5,9,9,12,15,21,23,31,32,45,50,61,66,87,94,114,
%T A308906 123,154,165,199,212,261,276,323,345,418,438,507,538,637,672,771,810,
%U A308906 947,999,1130,1192,1381,1445,1625,1716,1955,2045,2289,2399,2720
%N A308906 Sum of the smallest parts in the partitions of n into 6 squarefree parts.
%H A308906 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308906 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 * m, where mu is the Möbius function (A008683).
%F A308906 a(n) = A308903(n) - A308907(n) - A308908(n) - A308909(n) - A308910(n) - A308911(n).
%t A308906 Table[Sum[Sum[Sum[Sum[Sum[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 A308906 Cf. A008683, A308902, A308903, A308907, A308908, A308909, A308910, A308911.
%K A308906 nonn
%O A308906 0,9
%A A308906 _Wesley Ivan Hurt_, Jun 29 2019

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