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A326523
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Sum of all the 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, 9, 10, 22, 24, 52, 70, 120, 144, 221, 288, 418, 500, 714, 858, 1173, 1392, 1850, 2184, 2862, 3304, 4263, 4950, 6231, 7136, 8910, 10234, 12530, 14256, 17316, 19684, 23673, 26640, 31816, 35826, 42355, 47388, 55755, 62284, 72662
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OFFSET
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0,10
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LINKS
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FORMULA
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a(n) = 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, where mu is the Möbius function (A008683).
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MATHEMATICA
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Table[n*Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[MoebiusMu[q]^2 * MoebiusMu[p]^2 * MoebiusMu[o]^2 * MoebiusMu[m]^2 * MoebiusMu[l]^2 * MoebiusMu[k]^2 * MoebiusMu[j]^2 * MoebiusMu[i]^2*MoebiusMu[n - i - j - k - l - m - o - p - q]^2, {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 80}]
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CROSSREFS
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Cf. A008683, A326522, A326524, A326525, 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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