A334207 Number of ways to write 2n as the sum of two nonprime positive integers.

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

Offset

1,5

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to partitions

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