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A326444
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Sum of all the parts in the partitions of n into 8 squarefree parts.
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9
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0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 20, 22, 48, 65, 112, 135, 208, 255, 378, 456, 640, 756, 1034, 1219, 1632, 1875, 2444, 2835, 3640, 4147, 5220, 5952, 7392, 8382, 10234, 11550, 14004, 15688, 18810, 21021, 25040, 27798, 32802, 36421, 42680, 47160, 54832, 60489
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OFFSET
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0,9
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LINKS
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FORMULA
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a(n) = n * Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/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)^2, where mu is the Möbius function (A008683).
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MATHEMATICA
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Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[n * 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]^2, {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]
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CROSSREFS
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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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