A254671 - OEIS

A254671

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Apparently 8 and the elements of A061743. - R. J. Mathar, Feb 19 2015

LINKS

Table of n, a(n) for n=1..66.

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];

Select[Range[200], sol[#] != {}&] (* Jean-François Alcover, Jul 28 2020 *)

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))

print(aupto(113)) # Michael S. Branicky, Aug 11 2021

CROSSREFS

Cf. A254636 is the complement.

Sequence in context: A106670 A247463 A308562 * A265412 A372498 A345488

Adjacent sequences: A254668 A254669 A254670 * A254672 A254673 A254674

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Feb 04 2015

STATUS

approved