A308854 - OEIS

%I #14 Apr 19 2022 09:39:16

%S 0,0,0,0,0,0,0,0,0,0,10,11,12,26,28,45,48,51,54,95,80,126,132,161,144,

%T 250,182,297,252,348,330,527,352,594,442,700,504,888,570,1053,720,

%U 1189,882,1505,836,1710,1104,1927,1248,2303,1300,2703,1560,2862,1836

%N Sum of all the parts in the partitions of n into 5 primes.

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

%F a(n) = n * Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l), where c = A010051.

%F a(n) = n * A259195(n).

%F a(n) = A308855(n) + A308856(n) + A308857(n) + A308858(n) + A308859(n).

%t Table[Total[Flatten[Select[IntegerPartitions[n,{5}],AllTrue[#,PrimeQ]&]]],{n,0,60}] (* _Harvey P. Dale_, Apr 18 2022 *)

%Y Cf. A010051, A259195, A308855, A308856, A308857, A308858, A308859.

%K nonn

%O 0,11

%A _Wesley Ivan Hurt_, Jun 28 2019