A253775 Numbers representable as x^y + x + y, where x>1, y>1 are integers (without multiplicity).

8, 13, 14, 22, 32, 33, 39, 44, 58, 71, 72, 74, 88, 92, 112, 133, 134, 137, 158, 184, 212, 225, 242, 251, 264, 266, 274, 308, 344, 353, 382, 422, 464, 508, 523, 554, 602, 634, 652, 704, 738, 741, 758, 814, 872, 932, 994, 1013, 1033, 1036, 1058, 1124, 1192, 1262, 1306

Offset: 1

Author

Alex Ratushnyak, Jan 12 2015

Keywords

• nonn

Examples

			a(1) = 8 = 2^2 + 2 + 2.
a(2) = 13 = 2^3 + 2 + 3.
a(3) = 14 = 3^2 + 3 + 2.
a(4) = 22 = 2^4 + 2 + 4 = 4^2 + 4 + 2. - _Wolfdieter Lang_, Feb 03 2015
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A253776, A253777.

Programs

Maple

N:= 10000; # to get all terms <= N
select(`<=`,{seq(seq(x^y+x+y, y = 2..floor(log[x](N-x))),
      x=2..floor(sqrt(N)))},N);
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%, list)); # Robert Israel, Jan 14 2015

Mathematica

M = 2000;
Select[Table[x^y + x + y, {x, 2, Floor[Sqrt[M]]}, {y, 2, Floor[Log[x, M-x]] }] // Flatten, # <= M&] // Union (* Jean-François Alcover, Feb 27 2019, after Robert Israel *)