A326687 - OEIS

%I #10 Apr 07 2021 20:08:07

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,3,5,6,8,14,14,19,26,34,

%T 38,49,53,70,81,96,105,139,140,187,204,246,263,326,341,437,452,543,

%U 562,715,700,898,904,1100,1101,1387,1343,1720,1643,2037,1982

%N Sum of the second largest parts in the partitions of n into 10 primes.

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

%F a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} c(r) * 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-r) * i, where c is the prime characteristic (A010051).

%F a(n) = A326678(n) - A326679(n) - A326680(n) - A326681(n) - A326682(n) - A326683(n) - A326684(n) - A326685(n) - A326686(n) - A326688(n).

%t Table[Total[Select[IntegerPartitions[n,{10}],AllTrue[#,PrimeQ]&][[All,2]]],{n,0,70}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 04 2021 *)

%Y Cf. A010051, A259201, A326678, A326679, A326680, A326681, A326682, A326683, A326684, A326685, A326686, A326688.

%K nonn

%O 0,21

%A _Wesley Ivan Hurt_, Jul 17 2019