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A070110
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Numbers k such that [A070080(k), A070081(k), A070082(k)] is an integer triangle with relatively prime side lengths.
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14
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1, 2, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 32, 33, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 72, 73, 74, 75, 77
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OFFSET
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1,2
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COMMENTS
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A070084(a(k)) = gcd(A070080(a(k)), A070081(a(k)), A070082(a(k))) = 1;
all integer triangles [A070080(a(k)), A070081(a(k)), A070082(a(k))] are mutually nonisomorphic.
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LINKS
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Jean-François Alcover, Table of n, a(n) for n = 1..789
Reinhard Zumkeller, Integer-sided triangles
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EXAMPLE
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13 is a term: [A070080(13), A070081(13), A070082(13)]=[2,4,5], A070084(13)=gcd(2,4,5)=1.
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MATHEMATICA
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m = 50 (* 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_} /; GCD[a, b, c] == 1] // Flatten (* Jean-François Alcover, Oct 04 2021 *)
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CROSSREFS
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Cf. A051493, A070113, A070116, A070119, A070122, A070125, A070128, A070131, A070134, A070137, A070084.
Sequence in context: A190225 A276706 A271396 * A049095 A324583 A101742
Adjacent sequences: A070107 A070108 A070109 * A070111 A070112 A070113
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, May 05 2002
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STATUS
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approved
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