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A309469 Sum of the prime parts in the partitions of n into 8 parts.

%I A309469 #14 Jan 07 2022 11:38:10
%S A309469 0,0,0,0,0,0,0,0,0,2,7,11,28,41,79,115,191,255,389,517,752,976,1335,
%T A309469 1707,2289,2870,3737,4639,5904,7246,9088,11040,13635,16416,19984,
%U A309469 23856,28776,34054,40667,47796,56553,66043,77527,89992,104963,121151,140303
%N A309469 Sum of the prime parts in the partitions of n into 8 parts.
%H A309469 David A. Corneth, <a href="/A309469/b309469.txt">Table of n, a(n) for n = 0..9999</a>
%H A309469 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A309469 a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} (i * c(i) + j * c(j) + k * c(k) + l * c(l) + m * c(m) + o * c(o) + p * c(p) + (n-i-j-k-l-m-o-p) * c(n-i-j-k-l-m-o-p)), where c is the prime characteristic (A010051).
%t A309469 Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i (PrimePi[i] - PrimePi[i - 1]) + j (PrimePi[j] - PrimePi[j - 1]) + k (PrimePi[k] - PrimePi[k - 1]) + l (PrimePi[l] - PrimePi[l - 1]) + m (PrimePi[m] - PrimePi[m - 1]) + o (PrimePi[o] - PrimePi[o - 1]) + p (PrimePi[p] - PrimePi[p - 1]) + (n - i - j - k - l - m - o - p) (PrimePi[n - i - j - k - l - m - o - p] - PrimePi[n - i - j - k - l - m - o - p - 1]), {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]
%Y A309469 Cf. A010051, A309437, A309465, A309466, A309467, A309468, A309469, A309470, A309471.
%K A309469 nonn
%O A309469 0,10
%A A309469 _Wesley Ivan Hurt_, Aug 03 2019