A254034 Numbers representable as both b^c + b + c and x*y + x + y, where b, c, x, y are integers bigger than 1.

8, 14, 32, 39, 44, 71, 74, 92, 134, 137, 158, 184, 212, 242, 251, 264, 266, 274, 308, 344, 353, 422, 464, 523, 554, 602, 634, 704, 741, 758, 814, 872, 932, 994, 1013, 1033, 1036, 1058, 1124, 1262, 1334, 1484, 1562, 1642, 1724, 1743, 1808, 1894, 1982, 2072, 2164, 2197

Offset: 1

Author

Alex Ratushnyak, Jan 23 2015

Keywords

• nonn

Examples

			a(1) = 8 = 2^2 + 2 + 2 = 2*2 + 2 + 2.
a(2) = 14 = 3^2 + 3 + 2 = 4*2 + 4 + 2.
a(3) = 32 = 5^2 + 5 + 2 = 10*2 + 10 + 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A253916, A253917.

Programs

Maple

N:= 10000: # to get all entries <= N
A1:= {seq(seq(b^c+b+c, c = 2 .. floor(log[b](N))), b = 2 .. floor(sqrt(N)))}:
filter2:= proc(x) local x1;
   x1:= x+1;
   x <= N and not isprime(x1) and not(x1::even and isprime(x1/2))
end proc:
sort(convert(select(filter2,A1),list)); # Robert Israel, Dec 28 2020

Mathematica

mx = 2200; t = Transpose@ Flatten[ Table[{x^y + x + y, x*y + x + y}, {x, 2, Floor@ Sqrt@ mx}, {y, 2, Floor[mx/x]}], 1]; Intersection[ t[[1]], t[[2]]] (* Robert G. Wilson v, Jan 23 2015 *)