A246429 List of c, where c 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.

2, 3, 6, 4, 12, 5, 10, 15, 6, 20, 7, 14, 30, 21, 8, 28, 35, 24, 9, 42, 18, 40, 10, 36, 56, 45, 30, 11, 22, 63, 72, 33, 12, 44, 70, 55, 13, 66, 90, 26, 77, 60, 39, 88, 14, 99, 52, 84, 110, 65, 42, 15, 78, 30, 91, 70, 16, 104, 132, 60, 117, 130

Offset: 1

Author

Albert Lau, Sep 18 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, A247372 for list of b.

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, A247372.

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;
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