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A294487
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Sum of the lengths of the distinct rectangles with prime length and integer width such that L + W = n, W < L.
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1
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0, 0, 2, 3, 3, 5, 5, 12, 12, 7, 7, 18, 18, 24, 24, 24, 24, 41, 41, 60, 60, 49, 49, 72, 72, 59, 59, 59, 59, 88, 88, 119, 119, 102, 102, 102, 102, 120, 120, 120, 120, 161, 161, 204, 204, 181, 181, 228, 228, 228, 228, 228, 228, 281, 281, 281, 281, 252, 252, 311
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OFFSET
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1,3
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COMMENTS
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Sum of the largest parts of the partitions of n into two distinct parts with largest part prime.
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LINKS
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FORMULA
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a(n) = Sum_{i=1..floor((n-1)/2)} (n-i) * A010051(n-i).
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EXAMPLE
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a(14) = 24; the rectangles are 1 X 13 and 3 X 11 (7 X 7 is not considered since W < L). The sum of the lengths is then 13 + 11 = 24.
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MATHEMATICA
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Table[ Sum[(n - i)*(PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n-1)/2]}], {n, 60}]
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PROG
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(PARI) a(n) = sum(i=1, (n-1)\2, (n-i)*isprime(n-i)); \\ Michel Marcus, Nov 08 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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