A294113 Sum of the smaller parts of the partitions of 2n into two parts with larger part prime.
0, 3, 4, 4, 8, 6, 11, 8, 13, 20, 28, 24, 32, 25, 32, 41, 51, 42, 51, 40, 49, 60, 72, 60, 72, 84, 97, 111, 125, 109, 124, 107, 121, 136, 152, 169, 188, 169, 187, 206, 226, 204, 224, 199, 218, 238, 258, 229, 248, 268, 289, 312, 336, 306, 331, 357, 384, 412
Offset: 1
Examples
For n=7, 2n = 14 can be partitioned into two parts with the larger part prime as 13 + 1, 11 + 3, and 7 + 7. So a(7) = 1 + 3 + 7 = 11. - _Michael B. Porter_, Mar 14 2018
Links
Programs
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Maple
N:= 1000: # to get a(1)..a(n) P:= select(isprime, [2,seq(i,i=3..2*N,2)]): S:= ListTools:-PartialSums(P): f:= proc(n) local k1,k2; k1:= numtheory:-pi(2*n); k2:= numtheory:-pi(n-1); 2*n*(k1-k2) - S[k1] + S[k2] end proc: f(1):= 0: seq(f(n),n=1..N); # Robert Israel, Mar 13 2018 -
Mathematica
Table[Sum[i (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {i, n}], {n, 80}] -
PARI
a(n) = sum(k=1, n, k*isprime(2*n-k)); \\ Michel Marcus, Oct 24 2017
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PARI
a(n) = my(res = 0); forprime(p = n, 2*n, res+=(2*n - p)); res \\ David A. Corneth, Oct 24 2017