A070104 - OEIS

%I #15 Jul 27 2024 04:02:17

%S 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 8,16,11,18,11,17,14,21,12,25,18,25,15,30,19,32,20,32,25,38,23,40,28,

%U 41,28,47,31,51,34,46,40,55,35,61,44,58,41,68

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

%H Robert Israel, <a href="/A070104/b070104.txt">Table of n, a(n) for n = 1..10000</a>

%H R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>

%p f:= proc(n) local a,b,q,bmin,bmax,t;

%p   t:= 0;

%p   for a from 1 to n/3 do

%p     if n::even then bmin:= max(a+1,n/2-a+1) else bmin:= max(a+1,(n+1)/2-a) fi;

%p     q:= (n^2-2*n*a)/(2*(n-a));

%p     if q::integer then bmax:= min((n-a)/2, q-1) else bmax:= min((n-a)/2, floor(q)) fi;

%p     t:= t + nops(select(b -> igcd(a,b,n-a-b) = 1, [$bmin .. bmax]))

%p   od;

%p   t

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Jul 26 2024

%Y Cf. A070080, A070081, A070082, A070101, A051493, A005044, A070102, A024156, A070084, A070131.

%K nonn,look

%O 1,13

%A _Reinhard Zumkeller_, May 05 2002