A255265 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

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

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

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 *)

PROG

(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])

CROSSREFS