A255804 - OEIS

%I #6 Dec 07 2019 12:18:27

%S 264,308,8192,16400,88508,236684,504812,12127808,22491308,82310258

%N Numbers representable as x*y*(x+y), b*c+b+c, and d^e+d+e, where d>1, e>1, b>=c>1 and x>=y>1.

%C Intersection of A253775, A254671, A255265.

%e a(2) = 308 = 17^2 + 17 + 2 = 7 * 4 * (7 + 4) = 102 * 2 + 102 + 2.

%o (Python 2)

%o TOP = 100000000

%o a = [0]*TOP

%o c = []

%o for y in range(2, TOP/2):

%o   if 2**y + 2 + y >= TOP: break

%o for x in range(2, TOP/2):

%o     k = x**y+(x+y)

%o     if k>=TOP: break

%o     c.append(k)

%o for y in range(2, TOP/2):

%o   if 2*y*y*y >= TOP: break

%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   if y*(y+2) >= TOP: break

%o for x in range(y, TOP/2):

%o     k = x*y+(x+y)

%o     if k>=TOP: break

%o     a[k]|=2

%o     if a[k]==3 and (k in c): print k,

%o print [n for n in range(TOP) if a[n]==3 and (n in c)]

%Y Cf. A255267, A254034, A255265, A254671, A253775.

%K nonn,more

%O 1,1

%A _Alex Ratushnyak_, Mar 07 2015