A301384 Number of integer-sided triangles of area A188158(n).

1, 2, 2, 1, 2, 1, 2, 1, 4, 1, 1, 4, 2, 2, 2, 1, 4, 3, 1, 2, 1, 2, 4, 2, 2, 1, 1, 6, 3, 1, 5, 3, 3, 2, 2, 1, 4, 1, 2, 4, 8, 5, 1, 2, 1, 3, 1, 15, 2, 4, 2, 1, 5, 1, 6, 2, 1, 3, 4, 3, 1, 2, 2, 1, 2, 4, 5, 1, 5, 4, 1, 2, 3, 5, 1, 1, 1, 6, 2, 4, 2, 1, 2, 1, 17, 4, 1

Offset: 1

Author

Michel Lagneau, Mar 20 2018

Keywords

• nonn

Comments

Nonzero terms of A051584.

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Triangle

Crossrefs

Cf. A188158, A024153 (distinct side lengths), A051516, A051584, A051585.

Programs

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