A141095 Number of unordered pairs of coprime nonprime numbers that sum to 2n.

1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 1, 4, 1, 1, 1, 0, 3, 4, 1, 0, 4, 0, 4, 3, 0, 4, 5, 1, 1, 3, 1, 4, 6, 0, 0, 4, 1, 6, 6, 1, 5, 7, 1, 5, 3, 0, 8, 7, 0, 0, 10, 3, 9, 9, 0, 6, 5, 2, 8, 5, 2, 9, 10, 1, 5, 11, 2, 9, 12, 0, 3, 12, 4, 11, 5, 2, 12, 9, 1, 4, 14

Offset: 1

Author

T. D. Noe, Jun 02 2008

Keywords

• nonn
• look

Comments

Nonprime numbers are 1 and the composite numbers. See A141097 for pairs of coprime composite numbers. It appears that a(n) > 0 except for the 26 values of 2n given in A141096.

Examples

			a(17)=2 because 34 = 1+33 = 9+25.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10000
• Carlos Rivera, Conjecture 33: The Goldbach Temptation, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A141099, A141100.

Programs

Mathematica

Table[cnt=0; Do[If[GCD[2n-i,i]==1 && !PrimeQ[i] && !PrimeQ[2n-i], cnt++ ], {i,1,n,2}]; cnt, {n,100}]