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A308920 Sum of the smallest parts in the partitions of n into 6 primes.

%I A308920 #9 Oct 15 2021 15:02:55
%S A308920 0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,4,6,9,6,9,10,14,12,18,14,24,20,29,22,
%T A308920 41,24,48,34,57,36,69,40,85,48,90,54,120,58,132,70,150,76,176,82,202,
%U A308920 94,221,106,266,108,293,128,328,140,366,146,426,162,450
%N A308920 Sum of the smallest parts in the partitions of n into 6 primes.
%H A308920 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308920 a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-k-j-l-m) * m, where c = A010051.
%F A308920 a(n) = A308919(n) - A308921(n) - A308922(n) - A308923(n) - A308924(n) - A308925(n).
%t A308920 Table[Sum[Sum[Sum[Sum[Sum[m*(PrimePi[i] - PrimePi[i - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[l] - PrimePi[l - 1]) (PrimePi[m] - PrimePi[m - 1]) (PrimePi[n - i - j - k - l - m] - PrimePi[n - i - j - k - l - m - 1]), {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
%Y A308920 Cf. A010051, A259196, A308919, A308921, A308922, A308923, A308924, A308925.
%K A308920 nonn
%O A308920 0,13
%A A308920 _Wesley Ivan Hurt_, Jun 30 2019