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Numbers n such that neither n nor 2*n is representable as x*y+x+y, where x>=y>1.
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%I #10 May 10 2021 07:39:27

%S 0,1,2,3,5,6,9,18,21,30,33,36,78,81,96,105,138,141,156,165,198,210,

%T 228,261,270,273,306,330,336,345,366,378,393,438,453,498,525,546,561,

%U 576,585,600,606,618,660,690,726,765,810,828,861,876,933,936,966,996,1005,1008

%N Numbers n such that neither n nor 2*n is representable as x*y+x+y, where x>=y>1.

%o (Python)

%o TOP = 2200

%o a = [0]*TOP

%o for y in range(2, TOP//2):

%o for x in range(y, TOP//2):

%o k = x*y + x + y

%o if k>=TOP: break

%o a[k]=1

%o print([n for n in range(TOP//2) if a[n]==0 and a[2*n]==0])

%Y Cf. A254636, A255362.

%Y Cf. A064238 (also 3*n cannot be represented as x*y+x+y, x>=y>1).

%Y Cf. A237189 (also 3*n and 4*n cannot be represented as x*y+x+y, x>=y>1).

%K nonn

%O 1,3

%A _Alex Ratushnyak_, Mar 19 2015