A394958 Numbers k such that k = x*y = w*z with x + y and w - z squares.

0, 4, 20, 60, 64, 80, 84, 100, 136, 144, 150, 156, 196, 220, 224, 240, 260, 320, 324, 360, 380, 444, 580, 600, 660, 700, 736, 900, 960, 1020, 1024, 1040, 1056, 1100, 1260, 1280, 1344, 1404, 1440, 1476, 1484, 1600, 1620, 1640, 1680, 1736, 1780, 1824, 1884, 2020, 2100, 2176, 2304, 2400, 2436, 2480

Offset

1,2

Comments

If k is a term, then so is k * m^4 for all m.

All terms are even.

Links

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

Example

a(6) = 80 is a term because 80 = 80 * 1 = 20 * 4 with 80 + 1 = 81 = 9^2 and 20 - 4 = 16 = 4^2 squares.

Maple

filter:= proc(n) local D;
   D:= select(t -> t^2 >= n, NumberTheory:-Divisors(n));
   ormap(t -> issqr(t + n/t), D) and ormap(t -> issqr(t - n/t), D)
end proc:
filter(0):= true:
select(filter, [seq(i, i=0..10000, 2)]);

Crossrefs

0 and intersection of A218381 and A395626. Includes A013709.

Sequence in context: A196295 A196213 A196680 * A033488 A018211 A135507

Adjacent sequences: A394951 A394952 A394953 * A394959 A394960 A394961

Keyword

nonn,new

Author

Robert Israel, Jul 02 2026

Status

approved