A368058 Sum of the smaller parts of the partitions of n into two distinct parts with larger part prime.
0, 0, 1, 1, 2, 1, 2, 4, 6, 3, 4, 6, 8, 4, 6, 8, 10, 13, 16, 20, 24, 17, 20, 24, 28, 19, 22, 25, 28, 32, 36, 41, 46, 34, 38, 42, 46, 32, 36, 40, 44, 49, 54, 60, 66, 49, 54, 60, 66, 72, 78, 84, 90, 97, 104, 111, 118, 96, 102, 109, 116, 93, 100, 107, 114, 121, 128, 136, 144, 152, 160
Offset: 1
Keywords
Links
Programs
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Maple
N:= 100: # for a(1) .. a(N) V:= Vector(N): for i from 1 do p:= ithprime(i); if p >= N then break fi; m:= min(2*p-1,N); V[p+1..m]:= V[p+1..m] + <$1..m-p> od: convert(V,list); # Robert Israel, Jan 26 2024
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Mathematica
Table[Sum[i (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n - 1)/2]}],{n, 100}]
Formula
a(n) = Sum_{i=1..floor((n-1)/2)} i * c(n - i), where c is the prime characteristic (A010051).