A326545 - OEIS

%I #13 Jul 23 2021 22:10:26

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,4,4,7,9,10,12,18,17,23,24,

%T 30,30,45,43,59,60,75,75,106,94,130,124,165,152,210,180,257,229,307,

%U 278,386,320,463,400,547,464,654,539,784,643,896,749,1081

%N Sum of the fifth largest parts in the partitions of n into 9 primes.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F 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) * l, where c(n) is the prime characteristic (A010051).

%F a(n) = A326540(n) - A326541(n) -  A326542(n) - A326543(n) - A326544(n) - A326546(n) - A326547(n) - A326548(n) - A326549(n).

%t Table[Total[Select[IntegerPartitions[n,{9}],AllTrue[#,PrimeQ]&][[All,5]]],{n,0,70}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 09 2021 *)

%Y Cf. A010051, A259200, A326540, A326541, A326542, A326543, A326544, A326546, A326547, A326548, A326549.

%K nonn

%O 0,19

%A _Wesley Ivan Hurt_, Jul 13 2019