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A105659 Number of different characteristics, this is the squarefree part of (a+b+c)(a+b-c)(a-b+c)(-a+b+c), of integral triangles (a,b,c) with diameter n. 0
1, 2, 4, 5, 8, 11, 12, 16, 18, 22, 28, 28, 35, 38, 49, 50, 57, 65, 75, 74, 87, 83, 112, 111, 114, 120, 135, 146, 175, 168, 196, 185, 213, 222, 219, 234, 267, 270, 293, 306, 339, 333, 386, 348, 365, 420, 460, 431, 445, 436, 490, 480, 577, 511, 549, 559, 610, 635 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

a(3)=4 because the integral triangles with diameter 3 are (3,2,2), (3,3,1), (3,3,2), (3,3,3) and the characteristics are 7, 35, 2, 3.

MATHEMATICA

SquareFreePart[n_] := Times @@ Apply[Power, ({#1[[1]], Mod[#1[[2]], 2]} & ) /@ FactorInteger[n], {1}]; SquareFreePart[{a_, b_, c_}] := SquareFreePart[ (a+b+c)*(a+b-c)*(a-b+c)*(-a+b+c)]; ok[{a_, b_, c_}] := a-b < c < a+b && a-c < b < a+c && b-c < a < b+c; triangles[a_] := Reap[Do[ If[ok[{a, b, c}], Sow[{a, b, c}]], {b, 1, a}, {c, 1, b}]][[ 2, 1]]; a[n_] := Length[ Union[ SquareFreePart /@ triangles[n]]]; Table[a[n], {n, 1, 58}] (* Jean-Fran├žois Alcover, Sep 11 2012 *)

CROSSREFS

Sequence in context: A322125 A174803 A282434 * A298990 A191169 A191122

Adjacent sequences:  A105656 A105657 A105658 * A105660 A105661 A105662

KEYWORD

nonn

AUTHOR

Sascha Kurz, May 04 2005

STATUS

approved

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Last modified May 11 16:48 EDT 2021. Contains 343805 sequences. (Running on oeis4.)