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A141097 Number of unordered pairs of coprime composite numbers that sum to 2n. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A154312 A236076 A119900 * A278045 A096335 A191910

Adjacent sequences:  A141094 A141095 A141096 * A141098 A141099 A141100

KEYWORD

nonn

AUTHOR

T. D. Noe, Jun 02 2008

STATUS

approved

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Last modified May 26 01:26 EDT 2017. Contains 287073 sequences.