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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.
4
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
1,1
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, A247372 for list of b.
LINKS
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;
%[[;; , 3]]
CROSSREFS
Sequence in context: A351378 A104663 A358299 * A305325 A302848 A046202
KEYWORD
nonn,look
AUTHOR
Albert Lau, Sep 18 2014
STATUS
approved