OFFSET
1,2
COMMENTS
Nonzero terms of A051584.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Triangle
EXAMPLE
a(9) = 4 because A188158(9) = 60 corresponding to 4 triangles (a, b, c) = (6, 25, 29), (8, 15, 17), (10, 13, 13) and (13, 13, 24) of area 60.
MAPLE
A301384 := proc(A::integer)
local Asqr, s, a, b, c, sol ;
sol := 0 ;
Asqr := A^2 ;
for s in numtheory[divisors](Asqr) do
if s^2> A then
for a from 1 to s-1 do
if modp(Asqr, s-a) = 0 then
for b from a to s-1 do
c := 2*s-a-b ;
if s*(s-a)*(s-b)*(s-c) = Asqr and c >= b then
sol := sol+1 ;
end if;
end do:
end if;
end do:
end if;
end do:
sol ;
end proc:
for n from 3 to 600 do
a301384 := A301384(n) ;
if a301384 > 0 then
printf("%d, \n", a301384) ;
end if;
end do: # R. J. Mathar, May 02 2018
MATHEMATICA
nn=1000; lst={}; lst2={}; Do[s=(a+b+c)/2; If[IntegerQ[s], area2=s(s-a)(s-b)(s-c); If[0<area2<=nn^2&&IntegerQ[Sqrt[area2]], AppendTo[lst, Sqrt[area2]]]], {a, nn}, {b, a}, {c, b}]; lst1=Sort[lst]; n0=Length[lst]; i=1; Do[If[Part[lst1, t-1]==Part[lst1, t], i=i+1, AppendTo[lst2, i]; i=1], {t, 2, n0}]; lst2
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 20 2018
STATUS
approved