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A308857
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Sum of the third largest parts in the partitions of n into 5 primes.
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5
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 5, 5, 8, 7, 9, 8, 16, 12, 21, 20, 27, 20, 41, 27, 46, 34, 54, 44, 78, 44, 86, 59, 104, 65, 129, 79, 152, 96, 175, 115, 221, 117, 249, 157, 295, 170, 342, 179, 394, 214, 430, 243, 517, 245, 584, 307, 643, 332, 730, 352
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OFFSET
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0,11
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LINKS
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FORMULA
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a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l) * j, where c = A010051.
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MATHEMATICA
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Table[Total[Select[IntegerPartitions[n, {5}], AllTrue[#, PrimeQ]&][[All, 3]]], {n, 0, 70}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 06 2020 *)
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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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