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A308854
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Sum of all the 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, 10, 11, 12, 26, 28, 45, 48, 51, 54, 95, 80, 126, 132, 161, 144, 250, 182, 297, 252, 348, 330, 527, 352, 594, 442, 700, 504, 888, 570, 1053, 720, 1189, 882, 1505, 836, 1710, 1104, 1927, 1248, 2303, 1300, 2703, 1560, 2862, 1836
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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) = 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), where c = A010051.
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MATHEMATICA
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Table[Total[Flatten[Select[IntegerPartitions[n, {5}], AllTrue[#, PrimeQ]&]]], {n, 0, 60}] (* Harvey P. Dale, Apr 18 2022 *)
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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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