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

%I A255265 #22 Oct 01 2024 08:51:05
%S A255265 16,30,48,54,70,84,96,120,126,128,160,162,180,198,210,240,250,264,286,
%T A255265 308,324,330,336,384,390,420,432,448,462,468,510,520,540,546,560,576,
%U A255265 624,630,646,660,672,686,714,720,750,768,798,810,840,880,884,912,960,966,1008
%N A255265 Numbers representable as x*y*(x+y), where x>=y>1.
%H A255265 Robert Israel, <a href="/A255265/b255265.txt">Table of n, a(n) for n = 1..10000</a>
%e A255265 a(2) = 30 = 3*2*(3+2).
%e A255265 a(5) = 70 = 5*2*(5+2).
%p A255265 N:= 10^4: # for terms <= N
%p A255265 S:= {}:
%p A255265 for y from 2 to floor((N/2)^(1/3)) do
%p A255265   for x from y do
%p A255265     v:= x*y *(x+y);
%p A255265     if v > N then break fi;
%p A255265     S:= S union {v}
%p A255265 od od:
%p A255265 sort(convert(S,list)); # _Robert Israel_, Sep 30 2024
%t A255265 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 *)
%o A255265 (Python)
%o A255265 TOP = 10000
%o A255265 a = [0] * TOP
%o A255265 for y in range(2, TOP // 2):
%o A255265     for x in range(y, TOP // 2):
%o A255265         k = x * y * (x + y)
%o A255265         if k >= TOP:
%o A255265             break
%o A255265         a[k] += 1
%o A255265 print([n for n in range(TOP) if a[n] > 0])
%Y A255265 Cf. A254671.
%K A255265 nonn
%O A255265 1,1
%A A255265 _Alex Ratushnyak_, Feb 19 2015