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A309467 Sum of the prime parts in the partitions of n into 6 parts.

%I A309467 #17 Mar 17 2025 04:19:38
%S A309467 0,0,0,0,0,0,0,2,7,11,28,41,79,101,160,210,310,392,559,683,909,1126,
%T A309467 1464,1766,2250,2687,3345,3977,4853,5701,6886,8012,9522,11036,12979,
%U A309467 14888,17388,19842,22936,26053,29853,33725,38496,43219,48947,54800,61768,68800
%N A309467 Sum of the prime parts in the partitions of n into 6 parts.
%H A309467 David A. Corneth, <a href="/A309467/b309467.txt">Table of n, a(n) for n = 0..9999</a>
%H A309467 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A309467 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)} (i * c(i) + j * c(j) + k * c(k) + l * c(l) + m * c(m) + (n-i-j-k-l-m) * c(n-i-j-k-l-m)), where c is the prime characteristic (A010051).
%t A309467 Table[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]) + (n - i - j - k - l - m) (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, 80}]
%Y A309467 Cf. A010051, A309433, A309465, A309466, A309467, A309468, A309469, A309470, A309471.
%K A309467 nonn
%O A309467 0,8
%A A309467 _Wesley Ivan Hurt_, Aug 03 2019