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 A070112 Numbers n such that [A070080(n), A070081(n), A070082(n)] is a scalene integer triangle. 10
 8, 13, 17, 20, 21, 25, 29, 30, 33, 36, 37, 41, 42, 44, 45, 49, 50, 53, 56, 57, 59, 60, 62, 66, 67, 69, 70, 74, 75, 77, 78, 79, 80, 83, 86, 87, 89, 90, 92, 96, 97, 99, 100, 101, 102, 105, 106, 110, 111, 113, 114, 115, 116, 119, 122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Jean-François Alcover, Table of n, a(n) for n = 1..920 Reinhard Zumkeller, Integer-sided triangles EXAMPLE a(17)=50: [A070080(50), A070081(50), A070082(50)]=[4<6<8]. MATHEMATICA m = 55 (* max perimeter *); sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &]; triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1] & // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &]; Position[triangles, {a_, b_, c_} /; a < b < c] // Flatten (* Jean-François Alcover, Oct 12 2021 *) CROSSREFS Cf. A005044, A070113, A070114, A070121, A070122, A070123, A070130, A070131, A070132. Sequence in context: A129410 A338598 A168339 * A070113 A178968 A006613 Adjacent sequences:  A070109 A070110 A070111 * A070113 A070114 A070115 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 05 2002 STATUS approved

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Last modified May 25 02:55 EDT 2022. Contains 354047 sequences. (Running on oeis4.)