A255267 Numbers representable as both x*y*(x+y) and b*c+b+c, where b>=c>1 and x>=y>1.

48, 54, 84, 120, 128, 160, 264, 286, 308, 324, 384, 390, 468, 510, 560, 624, 686, 714, 720, 798, 840, 884, 912, 960, 1024, 1056, 1134, 1140, 1190, 1224, 1254, 1280, 1330, 1350, 1386, 1440, 1456, 1500, 1512, 1584, 1650, 1672, 1680, 1710, 1748, 1794, 1798, 1820, 1890

Offset: 1

Author

Alex Ratushnyak, Feb 19 2015

Keywords

• nonn

Comments

Intersection of A254671 and A255265.

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.

Examples

			a(3) = 84 = 4*3*(4+3) = 16*4 + 16 + 4.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..12033 (terms <= 2*10^6)
• David A. Corneth, PARI program

Crossrefs

Cf. A254671, A255265.

Programs

PARI

\\ See Corneth link

Python

TOP = 100000
a = [0]*TOP
b = [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
for y in range(2,TOP//2):
  for x in range(y,TOP//2):
    k = x*y+(x+y)
    if k>=TOP: break
    b[k]+=1
print([n for n in range(TOP) if a[n]>0 and b[n]>0])