A141096 -id:A141096 - cp's OEIS frontend

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

T. D. Noe, Jun 02 2008

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.

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

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

Cf. A141099, A141100.

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

A141098 Even numbers not representable as the sum of two coprime composite numbers.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 36, 38, 40, 42, 48, 50, 54, 56, 60, 66, 70, 72, 78, 80, 84, 90, 96, 108, 110, 120, 126, 132, 138, 140, 150, 180, 210

Offset: 1

T. D. Noe, Jun 02 2008

210 is the last term.

This sequence is a superset of A141096. See A141097.

t = Table[Length[Select[Range[2, n/2], ! PrimeQ[#] && ! PrimeQ[n - #] && GCD[#, n - #] == 1 &]], {n, 2, 2000, 2}]; Flatten[2*Position[t, 0]] (* T. D. Noe, Dec 05 2013 *)

A232721 Numbers not representable as the sum of two coprime nonprime numbers.

Original entry on oeis.org

1, 3, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 42, 48, 54, 60, 72, 80, 84, 90, 108, 110, 132, 138, 140, 150, 180

Offset: 1

Irina Gerasimova, Nov 28 2013

Numbers n such that A185279(n) = 0. 1 and 3 together with A141096.

Cf. A062303, A018252, A141095, A141098.

t = Table[Length[Select[Range[n/2], ! PrimeQ[#] && ! PrimeQ[n - #] && GCD[#, n - #] == 1 &]], {n, 2000}]; Flatten[Position[t, 0]] (* T. D. Noe, Dec 05 2013 *)

cp's OEIS Frontend

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

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A141098 Even numbers not representable as the sum of two coprime composite numbers.

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A232721 Numbers not representable as the sum of two coprime nonprime numbers.

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