

A254671


Numbers that can be represented as x * y + x + y, where x >= y > 1.


7



8, 11, 14, 15, 17, 19, 20, 23, 24, 26, 27, 29, 31, 32, 34, 35, 38, 39, 41, 43, 44, 47, 48, 49, 50, 51, 53, 54, 55, 56, 59, 62, 63, 64, 65, 67, 68, 69, 71, 74, 75, 76, 77, 79, 80, 83, 84, 86, 87, 89, 90, 91, 92, 94, 95, 97, 98, 99, 101, 103, 104, 107, 109, 110, 111, 113
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OFFSET

1,1


COMMENTS



LINKS



EXAMPLE

14 = 2 * 4 + 2 + 4.
15 = 3 * 3 + 3 + 3.
There is no way to express 16 in this form, so it is not in the sequence.


MATHEMATICA

sol[t_] := Solve[x >= y > 1 && x y + x + y == t, {x, y}, Integers];


PROG

(Python)
def aupto(limit):
cands = range(2, limit//3+1)
nums = [x*y+x+y for i, y in enumerate(cands) for x in cands[i:]]
return sorted(set(k for k in nums if k <= limit))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



