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

1,29

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.

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

Example

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

Mathematica

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

Crossrefs

Cf. A141099, A141100.

Sequence in context: A363899 A119900 A328376 * A278045 A096335 A191910

Adjacent sequences: A141094 A141095 A141096 * A141098 A141099 A141100

Keyword

nonn

Author

T. D. Noe, Jun 02 2008

Status

approved