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%I #9 May 09 2021 11:18:02
%S 48,54,84,120,128,160,264,286,308,324,384,390,468,510,560,624,686,714,
%T 720,798,840,884,912,960,1024,1056,1134,1140,1190,1224,1254,1280,1330,
%U 1350,1386,1440,1456,1500,1512,1584,1650,1672,1680,1710,1748,1794,1798,1820,1890
%N Numbers representable as both x*y*(x+y) and b*c+b+c, where b>=c>1 and x>=y>1.
%C Intersection of A254671 and A255265.
%C The subsequence of squares begins: 324, 1024, 2500, 3600, 11664, 19600, 20736, 36864, 63504, 82944, 129600, 153664, 230400, 236196, 250000, 291600, 345744, 419904, 777924, 810000, 944784.
%e a(3) = 84 = 4*3*(4+3) = 16*4 + 16 + 4.
%o (Python)
%o TOP = 100000
%o a = [0]*TOP
%o b = [0]*TOP
%o for y in range(2,TOP//2):
%o for x in range(y,TOP//2):
%o k = x*y*(x+y)
%o if k>=TOP: break
%o a[k]+=1
%o for y in range(2,TOP//2):
%o for x in range(y,TOP//2):
%o k = x*y+(x+y)
%o if k>=TOP: break
%o b[k]+=1
%o print([n for n in range(TOP) if a[n]>0 and b[n]>0])
%Y Cf. A254671, A255265.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, Feb 19 2015
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