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URL: https://oeis.org/A308774

⇱ A308774 - OEIS

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A308774
Sum of the largest parts in the partitions of n into 4 prime parts.
4
0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 8, 8, 12, 17, 12, 19, 23, 30, 38, 54, 31, 62, 59, 79, 73, 119, 71, 151, 113, 169, 115, 207, 102, 234, 171, 263, 168, 350, 191, 425, 220, 391, 265, 518, 246, 606, 322, 636, 383, 774, 348, 918, 477, 947, 516, 1102, 468, 1259
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) * (n-i-j-k), where c = A010051.
a(n) = A308809(n) - A308771(n) - A308772(n) - A308773(n).
MATHEMATICA
Table[Sum[Sum[Sum[(n - i - j - k) (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