A255265 Numbers representable as x*y*(x+y), where x>=y>1.

16, 30, 48, 54, 70, 84, 96, 120, 126, 128, 160, 162, 180, 198, 210, 240, 250, 264, 286, 308, 324, 330, 336, 384, 390, 420, 432, 448, 462, 468, 510, 520, 540, 546, 560, 576, 624, 630, 646, 660, 672, 686, 714, 720, 750, 768, 798, 810, 840, 880, 884, 912, 960, 966, 1008

Offset: 1

Author

Alex Ratushnyak, Feb 19 2015

Keywords

• nonn

Examples

			a(2) = 30 = 3*2*(3+2).
a(5) = 70 = 5*2*(5+2).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A254671.

Programs

Maple

N:= 10^4: # for terms <= N
S:= {}:
for y from 2 to floor((N/2)^(1/3)) do
  for x from y do
    v:= x*y *(x+y);
    if v > N then break fi;
    S:= S union {v}
od od:
sort(convert(S,list)); # Robert Israel, Sep 30 2024

Mathematica

r[n_] := Reduce[x >= y > 1 && n == x*y*(x+y), {x, y}, Integers]; Reap[For[n = 2, n <= 1000, n = n+2, If[r[n] =!= False, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Feb 26 2015 *)

Python

TOP = 10000
a = [0] * TOP
for y in range(2, TOP // 2):
    for x in range(y, TOP // 2):
        k = x * y * (x + y)
        if k >= TOP:
            break
        a[k] += 1
print([n for n in range(TOP) if a[n] > 0])