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A308809
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Sum of all the parts in the partitions of n into 4 primes.
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4
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0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 10, 22, 24, 26, 42, 30, 48, 51, 72, 76, 120, 63, 132, 115, 168, 125, 234, 135, 308, 203, 330, 217, 416, 198, 476, 315, 540, 296, 684, 351, 840, 410, 798, 473, 1056, 450, 1196, 564, 1248, 637, 1500, 612, 1768, 795, 1782, 880
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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_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} c(i) * c(j) * c(k) * c(n-i-j-k), where c = A010051.
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MATHEMATICA
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Table[n*Sum[Sum[Sum[(PrimePi[k] - PrimePi[k - 1])*(PrimePi[j] - PrimePi[j - 1]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i - j - k] - PrimePi[n - i - j - k - 1]), {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {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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