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A070104 Number of integer triangles with perimeter n and relatively prime side lengths which are obtuse and scalene.

%I A070104 #15 Jul 27 2024 04:02:17
%S A070104 0,0,0,0,0,0,0,0,1,0,1,0,2,1,2,2,3,1,4,3,6,2,7,4,8,4,8,6,10,6,12,8,14,
%T A070104 8,16,11,18,11,17,14,21,12,25,18,25,15,30,19,32,20,32,25,38,23,40,28,
%U A070104 41,28,47,31,51,34,46,40,55,35,61,44,58,41,68
%N A070104 Number of integer triangles with perimeter n and relatively prime side lengths which are obtuse and scalene.
%H A070104 Robert Israel, <a href="/A070104/b070104.txt">Table of n, a(n) for n = 1..10000</a>
%H A070104 R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>
%p A070104 f:= proc(n) local a,b,q,bmin,bmax,t;
%p A070104   t:= 0;
%p A070104   for a from 1 to n/3 do
%p A070104     if n::even then bmin:= max(a+1,n/2-a+1) else bmin:= max(a+1,(n+1)/2-a) fi;
%p A070104     q:= (n^2-2*n*a)/(2*(n-a));
%p A070104     if q::integer then bmax:= min((n-a)/2, q-1) else bmax:= min((n-a)/2, floor(q)) fi;
%p A070104     t:= t + nops(select(b -> igcd(a,b,n-a-b) = 1, [$bmin .. bmax]))
%p A070104   od;
%p A070104   t
%p A070104 end proc:
%p A070104 map(f, [$1..100]); # _Robert Israel_, Jul 26 2024
%Y A070104 Cf. A070080, A070081, A070082, A070101, A051493, A005044, A070102, A024156, A070084, A070131.
%K A070104 nonn,look
%O A070104 1,13
%A A070104 _Reinhard Zumkeller_, May 05 2002