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 A334207 Number of ways to write 2n as the sum of two nonprime positive integers. 1
 1, 0, 0, 1, 2, 2, 2, 4, 4, 4, 5, 6, 6, 7, 8, 7, 9, 11, 8, 11, 12, 11, 12, 14, 14, 14, 16, 15, 16, 19, 15, 19, 21, 17, 21, 22, 20, 22, 25, 22, 23, 27, 24, 25, 30, 26, 27, 31, 27, 31, 33, 30, 31, 34, 32, 34, 37, 34, 34, 42, 34, 37, 43, 36, 41, 43, 40, 41, 44, 43 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{i=1..n} (1 - c(i)) * (1 - c(2*n - i)), where c is the prime characteristic (A010051). EXAMPLE a(8) = 4; 2*8 = 16 has four partitions into nonprime parts, (15,1), (12,4), (10,6) and (8,8). MAPLE N:= 1000: # for a(1)..a(N) NP:= remove(isprime, [\$1..2*N]): V:= Vector(N): for i from 1 to nops(NP) do   for j from i do     x:= NP[i]+NP[j];     if x > 2*N then break fi;     if x::even then       V[x/2]:= V[x/2]+1;     fi od od: convert(V, list); # Robert Israel, Apr 20 2020 MATHEMATICA Table[Sum[(1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[2 n - i] + PrimePi[2 n - i - 1]), {i, n}], {n, 100}] CROSSREFS Cf. A010051. Bisection of A062610. Sequence in context: A240321 A054861 A187324 * A323094 A086227 A302402 Adjacent sequences:  A334204 A334205 A334206 * A334208 A334209 A334210 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Apr 18 2020 STATUS approved

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Last modified July 27 15:47 EDT 2021. Contains 346307 sequences. (Running on oeis4.)