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A326546 Sum of the fourth largest parts in the partitions of n into 9 primes.

%I A326546 #10 Mar 09 2023 20:48:16
%S A326546 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,5,7,10,10,14,18,19,23,30,
%T A326546 32,38,49,54,65,74,83,97,120,118,148,159,189,193,242,231,299,293,359,
%U A326546 357,454,407,543,517,649,600,788,706,952,851,1102,1004,1351
%N A326546 Sum of the fourth largest parts in the partitions of n into 9 primes.
%H A326546 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A326546 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) * k, where c is the prime characteristic (A010051).
%F A326546 a(n) = A326540(n) - A326541(n) - A326542(n) - A326543(n) - A326544(n) - A326545(n) - A326547(n) - A326548(n) - A326549(n).
%t A326546 Table[Total[Select[IntegerPartitions[n,{9}],AllTrue[#,PrimeQ]&][[;;,4]]],{n,0,70}] (* _Harvey P. Dale_, Mar 09 2023 *)
%Y A326546 Cf. A010051, A259200, A326540, A326541, A326542, A326543, A326544, A326545, A326547, A326548, A326549.
%K A326546 nonn
%O A326546 0,19
%A A326546 _Wesley Ivan Hurt_, Jul 13 2019