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URL: https://oeis.org/A308771

⇱ A308771 - OEIS

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A308771
Sum of the smallest parts of the partitions of n into 4 prime parts.
4
0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 5, 4, 7, 4, 8, 6, 10, 8, 18, 6, 18, 10, 21, 10, 28, 10, 38, 14, 34, 14, 47, 12, 51, 18, 55, 16, 68, 18, 81, 20, 73, 22, 105, 20, 110, 24, 113, 26, 136, 24, 161, 30, 147, 32, 187, 28, 200, 34, 204, 32, 237, 32, 262, 38, 246
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) * k, where c = A010051.
a(n) = A308809(n) - A308772(n) - A308773(n) - A308774(n).
MATHEMATICA
Table[Sum[Sum[Sum[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