cp's OEIS Frontend

A326544 Sum of the sixth largest parts of the partitions of n into 9 primes.

%I A326544 #13 Aug 31 2025 15:28:30
%S A326544 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,4,6,9,9,12,16,17,21,24,
%T A326544 26,30,38,41,49,56,62,71,88,88,107,114,133,138,173,162,206,205,247,
%U A326544 246,311,282,372,352,438,404,527,469,624,553,716,641,862,731
%N A326544 Sum of the sixth largest parts of the partitions of n into 9 primes.
%H A326544 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326544 a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} c(q) * c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p-q) * m, where c = A010051.
%F A326544 a(n) = A326540(n) - A326541(n) - A326542(n) - A326543(n) - A326545(n) - A326546(n) - A326547(n) - A326548(n) - A326549(n).
%t A326544 Table[Total[Select[IntegerPartitions[n,{9}],AllTrue[#,PrimeQ]&][[All,6]]],{n,0,70}] (* _Harvey P. Dale_, Jan 01 2023 *)
%Y A326544 Cf. A010051, A259200, A326540, A326541, A326542, A326543, A326545, A326546, A326547, A326548, A326549.
%K A326544 nonn,changed
%O A326544 0,19
%A A326544 _Wesley Ivan Hurt_, Jul 13 2019