A247372 List of b, where b is positive integer solutions of 1/a + 1/b = 1/c and a>b>c and gcd(a,b,c)=1, sorted by ascending a, then b.

3, 4, 10, 5, 21, 6, 14, 24, 7, 36, 8, 18, 55, 30, 9, 44, 60, 33, 10, 78, 22, 65, 11, 52, 105, 70, 39, 12, 26, 112, 136, 42, 13, 60, 119, 80, 14, 102, 171, 30, 126, 85, 48, 152, 15, 180, 68, 133, 210, 90, 51, 16, 114, 34, 140, 95, 17, 168, 253, 76, 198, 230

Offset: 1

Author

Albert Lau, Sep 14 2014

Keywords

• nonn
• look

Comments

For any positive integer m and n, a=m(m+n), b=n(m+n), c=m*n is an integer solution for 1/a + 1/b = 1/c.

See A106430 for list of a, A246429 for list of c.

Examples

			1/6 + 1/3 = 1/2.
1/12 + 1/4 = 1/3.
1/15 + 1/10 = 1/6.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A106430, A246429.

Programs

Mathematica

aMax = 300;
Select[Sequence @@@ Table[{m (m + n), n (m + n), m n}, {m, Sqrt[aMax]}, {n, Min[m - 1, aMax/m - m]}], GCD @@ # == 1 &] // Sort;
%[[;;, 2]]