|
%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
| 