Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Oct 19 2024 22:01:48
%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.
%H David A. Corneth, <a href="/A255267/b255267.txt">Table of n, a(n) for n = 1..12033</a> (terms <= 2*10^6)
%H David A. Corneth, <a href="/A255267/a255267.gp.txt">PARI program</a>
%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])
%o (PARI) \\ See Corneth link
%Y Cf. A254671, A255265.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, Feb 19 2015