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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.
1

%I #19 Nov 14 2024 10:22:48

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

%T 227240552,385278014,1069061114,2363758544,2591166314,2985365684,

%U 3310448834,4042988642,4791339182,5712714308,7553782658,8626601522,12494656622,14498688512,15165306758,15445891244

%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.

%H David A. Corneth, <a href="/A255804/b255804.txt">Table of n, a(n) for n = 1..160</a>

%H David A. Corneth, <a href="/A255804/a255804.gp.txt">PARI program</a>

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

%o (Python)

%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, end=', ')

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

%o (PARI) \\ See Corneth link

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

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Mar 07 2015

%E More terms from _David A. Corneth_, Oct 18 2024