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A235341 Positive integers a such that there exist b, c with 1/a + 1/b + 1/c = 1/3 and a >= b >= c. 0

%I #18 Feb 01 2014 15:33:38

%S 9,12,15,18,20,21,24,28,30,36,42,45,48,60,84,120,156

%N Positive integers a such that there exist b, c with 1/a + 1/b + 1/c = 1/3 and a >= b >= c.

%C See A236681 for motivation.

%e The solutions are {[9, 9, 9], [12, 8, 8], [15, 10, 6], [18, 9, 6], [20, 12, 5], [21, 7, 7], [24, 8, 6], [28, 21, 4], [30, 10, 5], [36, 18, 4], [42, 7, 6], [45, 9, 5], [48, 16, 4], [60, 15, 4], [84, 14, 4], [120, 8, 5], [156, 13, 4]}.

%o (PARI) S=1/3; for(a=1+1\S, 999, for(b=ceil(2/(S-1/a)), a, numerator(S-1/a-1/b)==1 && print1(a", ")+next(2)))

%K nonn,fini,full

%O 1,1

%A _M. F. Hasler_, Jan 30 2014

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