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A326525
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Sum of the eighth largest parts in the partitions of n into 9 squarefree parts.
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10
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 8, 9, 14, 18, 24, 28, 39, 46, 60, 69, 90, 105, 133, 149, 189, 216, 264, 297, 364, 412, 494, 553, 661, 743, 877, 972, 1149, 1280, 1493, 1650, 1922, 2126, 2454, 2702, 3107, 3429, 3916, 4291, 4895, 5374, 6086, 6647
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OFFSET
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0,12
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LINKS
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FORMULA
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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 * p, where mu is the Möbius function (A008683).
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MATHEMATICA
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Table[Total[Select[IntegerPartitions[n, {9}], AllTrue[#, SquareFreeQ]&][[;; , 8]]], {n, 0, 60}] (* Harvey P. Dale, Jan 30 2024 *)
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CROSSREFS
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Cf. A008683, A326522, A326523, A326524, A326526, A326527, A326528, A326529, A326530, A326531, A326532.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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