A350883 Sum of the smaller parts of the partitions of n into two prime parts.
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
Keywords
Examples
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.
Programs
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PARI
a(n) = sum(k=1, n\2, if (isprime(k) && isprime(n-k), k)); \\ Michel Marcus, Jan 21 2022