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A350883
Sum of the smaller parts of the partitions of n into two prime parts.
1
0, 0, 0, 0, 2, 2, 3, 2, 3, 2, 8, 0, 5, 2, 10, 2, 8, 0, 12, 2, 10, 2, 19, 0, 23, 2, 23, 0, 16, 0, 31, 2, 16, 2, 36, 0, 42, 0, 26, 2, 31, 0, 48, 2, 23, 2, 48, 0, 59, 2, 42, 0, 39, 0, 71, 2, 35, 0, 62, 0, 108, 2, 53, 2, 59, 0, 96, 0, 38, 2, 83, 0, 108, 2, 91, 2, 77, 0, 127
OFFSET
0,5
FORMULA
a(n) = Sum_{k=1..floor(n/2)} c(k) * c(n-k) * k, where c = A010051.
a(n) = Sum_{k=floor((n-1)^2/4)+1..floor(n^2/4)} c(2k-1) * c(2k) * A339399(2k-1), where c = A350866.
EXAMPLE
a(10) = 8; The partitions of 10 into two prime parts are (7,3) and (5,5). The sum of the smaller parts of these partitions is then 5+3 = 8.
PROG
(PARI) a(n) = sum(k=1, n\2, if (isprime(k) && isprime(n-k), k)); \\ Michel Marcus, Jan 21 2022
CROSSREFS
Cf. A010051, A339399, A350865 (larger parts), A350866.
Sequence in context: A342905 A356741 A152872 * A072832 A080328 A245555
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 20 2022
STATUS
approved