An evil number has an even number of 1s in its binary expansion. For example, 9 = 1001 has two 1-bits, so 9 is evil. The complementary set — odd popcount — are the odious numbers, and together they partition the non-negative integers.
The names are wordplay (evil / odious echo even / odd), coined in the analysis of the game of Kayles and popularized via combinatorial game theory. The evil/odious split underlies the Thue–Morse sequence: its \(n\)-th term is 0 exactly when \(n\) is evil.