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A070084 Greatest common divisor of sides of integer triangles [A070080(n), A070081(n), A070082(n)], sorted by perimeter, sides lexicographically ordered. 21
1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 7, 2, 1, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n)>1 iff there exists a smaller similar triangle [A070080(k), A070081(k), A070082(k)] with k<n and A070080(n)=A070080(k)*a(n), A070081(n)=A070081(k)*a(n) and A070082(n)=A070082(k)*a(n).

LINKS

Table of n, a(n) for n=1..90.

R. Zumkeller, Integer-sided triangles

FORMULA

a(n) = GCD(A070080(n), A070081(n), A070082(n)).

MATHEMATICA

maxPer = 22; maxSide = Floor[(maxPer - 1)/2]; order[{a_, b_, c_}] := (a + b + c)*maxPer^3 + a*maxPer^2 + b*maxPer + c; triangles = Reap[Do[If[a + b + c <= maxPer && c - b < a < c + b && b - a < c < b + a && c - a < b < c + a, Sow[{a, b, c}]], {a, 1, maxSide}, {b, a, maxSide}, {c, b, maxSide}]][[2, 1]]; GCD @@@ Sort[triangles, order[#1] < order[#2] &] (* Jean-Fran├žois Alcover, May 27 2013 *)

CROSSREFS

Cf. A051493, A005044, A070091, A070094, A070102, A070109, A070110, A070113, A070116, A070119, A070128, A070137.

Sequence in context: A014649 A279817 A253642 * A268372 A298848 A193518

Adjacent sequences:  A070081 A070082 A070083 * A070085 A070086 A070087

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2002

STATUS

approved

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Last modified January 24 06:20 EST 2019. Contains 319415 sequences. (Running on oeis4.)