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A057097
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Products of the three sides of Pythagorean triangles divided by 60.
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3
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1, 8, 13, 27, 34, 64, 70, 104, 125, 203, 216, 246, 259, 272, 343, 351, 512, 560, 671, 729, 832, 918, 1000, 1092, 1113, 1331, 1547, 1624, 1625, 1728, 1890, 1968, 2002, 2072, 2176, 2197, 2744, 2808, 3164, 3212, 3333, 3375, 3927, 4096, 4250, 4459, 4480
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OFFSET
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1,2
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COMMENTS
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Note that if m appears in the sequence then k^3*m will also appear for all k and so in particular all cubes appear; the reverse is not always true (for example, 32*255*257/60 = 34952 = 2^3*4369 eventually appears, but 4369 does not).
By considering the Pythagorean triangle (3k, 4k, 5k) we see that all numbers k^3 are in the sequence. - Sergey Pavlov, Mar 29 2017
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 3*4*5/60 = 1.
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MATHEMATICA
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(k=600000; lst={}; Do[Do[If[IntegerQ[a=Sqrt[c^2 - b^2]], If[a>=b, Break[]]; x=a b c; If[x<=k, AppendTo[lst, x]]], {b, c - 1, 4, -1}], {c, 5, 400, 1}]; Union@lst)/60 (* Vincenzo Librandi Mar 30 2017 *)
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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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