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A343281
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Numbers of the form x + y + z in positive integers x,y,z such that (x+y) | x*y, (y+z) | y*z, and (x+z) | x*z.
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0
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6, 12, 15, 18, 20, 24, 28, 30, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 66, 70, 72, 75, 77, 78, 80, 84, 88, 90, 91, 96, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 120, 126, 130, 132, 135, 138, 140, 143, 144, 150, 153, 154, 156, 160, 162, 165, 168, 170, 174, 175, 176, 180, 182, 184
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OFFSET
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1,1
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COMMENTS
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Not the same as A005279, this sequence contains 184.
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LINKS
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FORMULA
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a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} c(i*j/(i+j)) * c(i*(n-i-j)/(n-j)) * c(j*(n-i-j)/(n-i)), where c(n) = 1 - ceiling(n) + floor(n).
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EXAMPLE
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184 = [120,40,24] so that (120+40) | 120*40, (40+24) | 40*24, (120+24) | 120*24.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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