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%I #9 Mar 23 2023 07:32:09
%S 0,0,0,0,0,0,0,0,0,1,1,2,2,4,5,8,9,13,17,23,26,36,42,55,63,80,93,119,
%T 131,165,188,230,255,312,351,420,466,555,620,731,804,945,1046,1216,
%U 1333,1550,1702,1959,2141,2452,2688,3064,3334,3790,4136,4673,5070
%N Sum of the smallest parts of the partitions of n into 9 squarefree parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} mu(q)^2 * mu(p)^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-p-q)^2 * q, where mu is the Möbius function (A008683).
%F a(n) = A326523(n) - A326525(n) - A326526(n) - A326527(n) - A326528(n) - A326529(n) - A326530(n) - A326531(n) - A326532(n).
%t Table[Total[Select[IntegerPartitions[n,{9}],AllTrue[#,SquareFreeQ]&][[;;,-1]]],{n,0,60}] (* _Harvey P. Dale_, Mar 22 2023 *)
%Y Cf. A008683, A326522, A326523, A326525, A326526, A326527, A326528, A326529, A326530, A326531, A326532.
%K nonn
%O 0,12
%A _Wesley Ivan Hurt_, Jul 11 2019
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