A230035 Numbers which can be represented as a sum of 3 relatively prime positive integers such that each pair of them is not coprime.

31, 37, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 86, 87, 89, 91, 92, 93, 95, 97, 99, 101, 103, 106, 107, 109, 111, 113, 115, 116, 117, 118, 119, 121, 122, 123, 125, 127, 128, 129, 131, 133, 134, 135, 136, 137, 139, 141, 143

Offset: 1

Author

Vladimir Letsko, Dec 20 2013

Keywords

• nonn

Comments

The complement of A230034.

Each number beginning from 2731 is in a(n).

Generally for every positive integer k there is only finite quantity of numbers which can't be represented as a sum of k+1 relatively prime positive integers such that any k of them are not coprime.

For instance, for k = 3 570570 is the largest number which cannot be represented.

Examples

			31 is in a(n) because 31 = 6 + 10 + 15  and gcd(6, 10, 15) = 1 however gcd(6, 10) = 2, gcd(6, 15) = 3,  gcd(10, 15) = 5.
		

Crossrefs

Cf. A230034, A284825.