A pernicious number has a prime number of 1s in its binary representation. For example, 6 = 110 has two 1-bits, and 2 is prime — so 6 is pernicious; 7 = 111 has three, also prime.
Every number of the form \(2^k + 1\) (with \(k \ge 1\)) is pernicious (two 1-bits), and no power of two can ever be pernicious (one 1-bit; 1 is not prime).