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A308772
Sum of the third largest parts of the partitions of n into 4 prime parts.
4
0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 5, 5, 5, 7, 6, 8, 10, 12, 13, 20, 11, 20, 20, 27, 18, 34, 21, 44, 28, 44, 31, 59, 30, 65, 46, 79, 41, 96, 49, 115, 58, 117, 64, 157, 64, 170, 73, 179, 80, 214, 80, 243, 98, 245, 114, 307, 106, 332, 124, 352, 124, 399, 124
OFFSET
0,9
FORMULA
a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} c(k) * c(j) * c(i) * c(n-i-j-k) * j, where c = A010051.
a(n) = A308809(n) - A308771(n) - A308773(n) - A308774(n).
MATHEMATICA
Table[Sum[Sum[Sum[j (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, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 23 2019
STATUS
approved