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A294111
Sum of the smaller parts of the partitions of n into two parts with larger part prime.
2
0, 0, 1, 3, 2, 4, 2, 4, 6, 8, 4, 6, 8, 11, 6, 8, 10, 13, 16, 20, 24, 28, 20, 24, 28, 32, 22, 25, 28, 32, 36, 41, 46, 51, 38, 42, 46, 51, 36, 40, 44, 49, 54, 60, 66, 72, 54, 60, 66, 72, 78, 84, 90, 97, 104, 111, 118, 125, 102, 109, 116, 124, 100, 107, 114
OFFSET
1,4
FORMULA
a(n) = Sum_{i=1..floor(n/2)} i * c(n - i), where c is the prime characteristic (A010051).
MATHEMATICA
Table[Sum[i (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[n/2]}], {n, 80}]
Table[Total[Select[IntegerPartitions[n, {2}], PrimeQ[#[[1]]]&][[All, 2]]], {n, 70}] (* Harvey P. Dale, Feb 05 2023 *)
CROSSREFS
Sequence in context: A089214 A057038 A175798 * A372715 A373556 A349322
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 22 2017
STATUS
approved