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A326456 Sum of the smallest parts of the partitions of n into 8 primes.

%I A326456 #14 May 16 2025 15:04:45
%S A326456 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,4,6,8,8,11,12,15,16,22,18,26,
%T A326456 28,36,32,47,38,59,52,71,60,93,68,109,86,128,96,157,112,190,132,210,
%U A326456 154,262,168,300,198,344,224,399,246,464,286,515,324,605
%N A326456 Sum of the smallest parts of the partitions of n into 8 primes.
%H A326456 Harvey P. Dale, <a href="/A326456/b326456.txt">Table of n, a(n) for n = 0..199</a>
%H A326456 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326456 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)} c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p) * p, where c = A010051.
%F A326456 a(n) = A326455(n) - A326457(n) - A326458(n) - A326459(n) - A326460(n) - A326461(n) - A326462(n) - A326463(n).
%t A326456 Table[Total[Select[IntegerPartitions[n,{8}],AllTrue[#,PrimeQ]&][[;;,-1]]],{n,0,70}] (* _Harvey P. Dale_, Mar 28 2025 *)
%Y A326456 Cf. A010051, A259198, A326455, A326457, A326458, A326459, A326460, A326461, A326462, A326463.
%K A326456 nonn
%O A326456 0,17
%A A326456 _Wesley Ivan Hurt_, Jul 06 2019