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A308100
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Sum of the largest sides of all integer-sided triangles with prime sides and perimeter n.
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0
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0, 0, 0, 0, 0, 2, 3, 3, 3, 0, 5, 5, 5, 0, 12, 7, 14, 0, 7, 0, 7, 0, 11, 11, 22, 0, 37, 13, 37, 0, 26, 0, 24, 0, 47, 17, 47, 0, 85, 19, 91, 0, 74, 0, 55, 0, 105, 23, 107, 0, 82, 0, 88, 0, 42, 0, 65, 0, 133, 29, 81, 0, 172, 31, 234, 0, 153, 0, 143, 0, 120, 0
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OFFSET
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1,6
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LINKS
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FORMULA
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a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * A010051(i) * A010051(k) * A010051(n-i-k) * (n-i-k).
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MATHEMATICA
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Table[Sum[Sum[(n - i - k) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[n - i - k] - PrimePi[n - i - k - 1]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
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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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