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A308975 Sum of the smallest parts of the partitions of n into 7 primes.

%I A308975 #11 Mar 11 2025 08:47:20
%S A308975 0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,4,6,8,9,8,13,12,18,16,20,20,32,
%T A308975 24,37,32,45,38,63,44,74,52,84,62,109,66,123,84,145,94,173,102,209,
%U A308975 120,225,136,272,146,309,172,343,190,405,206,466,232,499,262
%N A308975 Sum of the smallest parts of the partitions of n into 7 primes.
%H A308975 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308975 a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} c(i) * c(j) * c(k) * c(l) * c(m) * c(o) * c(n-i-j-k-l-m-o) * o, where c = A010051.
%F A308975 a(n) = A308974(n) - A308976(n) - A308977(n) - A308978(n) - A308979(n) - A307637(n) - A308980(n).
%t A308975 Table[Sum[Sum[Sum[Sum[Sum[Sum[o*(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[o] - PrimePi[o - 1]) (PrimePi[n - i - j - k - l - m - o] - PrimePi[n - i - j - k - l - m - o - 1]), {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]
%Y A308975 Cf. A010051, A259197, A307637, A308974, A308976, A308977, A308978, A308979, A308980.
%K A308975 nonn
%O A308975 0,15
%A A308975 _Wesley Ivan Hurt_, Jul 04 2019