A350865 - OEIS

%I #12 Jan 27 2022 21:06:49

%S 0,0,0,0,2,3,3,5,5,7,12,0,7,11,18,13,24,0,24,17,30,19,47,0,49,23,55,0,

%T 40,0,59,29,48,31,100,0,102,0,50,37,89,0,120,41,109,43,136,0,181,47,

%U 158,0,117,0,199,53,133,0,170,0,252,59,133,61,261,0,300,0,98,67,267,0

%N Sum of the larger parts in the partitions of n into two prime parts.

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

%F a(n) = Sum_{k=1..floor(n/2)} c(k) * c(n-k) * (n-k), where c = A010051.

%F a(n) = Sum_{k=floor((n-1)^2/4)+1..floor(n^2/4)} c(2k-1) * c(2k) * A339399(2k), where c = A350866.

%e a(10) = 12; The partitions of 10 into two prime parts are (7,3) and (5,5). The sum of the larger parts of these partitions is then 7+5 = 12.

%o (PARI) a(n) = sum(k=1, n\2, if (isprime(k) && isprime(n-k), n-k)); \\ _Michel Marcus_, Jan 21 2022

%Y Cf. A010051, A061358, A339399, A350866, A350883 (smaller parts).

%K nonn

%O 0,5

%A _Wesley Ivan Hurt_, Jan 19 2022