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A255804 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.

%I A255804 #19 Nov 14 2024 10:22:48
%S A255804 264,308,8192,16400,88508,236684,504812,12127808,22491308,82310258,
%T A255804 227240552,385278014,1069061114,2363758544,2591166314,2985365684,
%U A255804 3310448834,4042988642,4791339182,5712714308,7553782658,8626601522,12494656622,14498688512,15165306758,15445891244
%N A255804 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 A255804 Intersection of A253775, A254671, A255265.
%H A255804 David A. Corneth, <a href="/A255804/b255804.txt">Table of n, a(n) for n = 1..160</a>
%H A255804 David A. Corneth, <a href="/A255804/a255804.gp.txt">PARI program</a>
%e A255804 a(2) = 308 = 17^2 + 17 + 2 = 7 * 4 * (7 + 4) = 102 * 2 + 102 + 2.
%o A255804 (Python)
%o A255804 TOP = 100000000
%o A255804 a = [0]*TOP
%o A255804 c = []
%o A255804 for y in range(2, TOP//2):
%o A255804   if 2**y + 2 + y >= TOP: break
%o A255804   for x in range(2, TOP//2):
%o A255804     k = x**y+(x+y)
%o A255804     if k>=TOP: break
%o A255804     c.append(k)
%o A255804 for y in range(2, TOP//2):
%o A255804   if 2*y*y*y >= TOP: break
%o A255804   for x in range(y, TOP//2):
%o A255804     k = x*y*(x+y)
%o A255804     if k>=TOP: break
%o A255804     a[k]=1
%o A255804 for y in range(2, TOP//2):
%o A255804   if y*(y+2) >= TOP: break
%o A255804   for x in range(y, TOP//2):
%o A255804     k = x*y+(x+y)
%o A255804     if k>=TOP: break
%o A255804     a[k]|=2
%o A255804     # if a[k]==3 and (k in c): print(k, end=', ')
%o A255804 print([n for n in range(TOP) if a[n]==3 and (n in c)])
%o A255804 (PARI) \\ See Corneth link
%Y A255804 Cf. A255267, A254034, A255265, A254671, A253775.
%K A255804 nonn
%O A255804 1,1
%A A255804 _Alex Ratushnyak_, Mar 07 2015
%E A255804 More terms from _David A. Corneth_, Oct 18 2024