A141097 Number of unordered pairs of coprime composite numbers that sum to 2n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 1, 3, 0, 1, 0, 0, 3, 3, 0, 0, 3, 0, 3, 2, 0, 3, 4, 0, 1, 2, 1, 4, 5, 0, 0, 3, 1, 5, 5, 0, 4, 6, 0, 5, 2, 0, 7, 6, 0, 0, 9, 2, 8, 8, 0, 6, 4, 1, 8, 4, 1, 9, 9, 1, 4, 10, 2, 8, 11, 0, 3, 11, 3, 10, 4, 2, 12, 8, 1, 4, 13, 2

Offset: 1

Author

T. D. Noe, Jun 02 2008

Keywords

• nonn

Comments

See A141095 for pairs of coprime nonprime numbers. It appears that a(n) > 0 except for the 43 values of 2n given in A141098. Roberts says that A. M. Vaidya proved that a(n) > 0 for all sufficiently large n.

Examples

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

References

• Joe Roberts, "Lure of the Integers", The Mathematical Association of America, 1992, p. 190.

Links

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

Crossrefs

Cf. A141099, A141100.

Programs

Mathematica

Table[cnt=0; Do[If[GCD[2n-i,i]==1 && !PrimeQ[i] && !PrimeQ[2n-i], cnt++ ], {i,3,n,2}]; cnt, {n,100}]