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

1,1

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.

Links

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

Example

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

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]]

Crossrefs

Cf. A106430, A246429.

Sequence in context: A063930 A183170 A014411 * A143443 A139556 A191150

Adjacent sequences: A247369 A247370 A247371 * A247373 A247374 A247375

Keyword

nonn,look

Author

Albert Lau, Sep 14 2014

Status

approved