Twenty-one is a Fibonacci number, a Harshad number, a Motzkin number, a triangular number and an octagonal number, as well as a composite number.
21 appears in the Padovan sequence, preceded by the terms 9, 12, 16 (it is the sum of the first two of these).
Adding up the sums of divisors for the integers 1 through 5 yields 21.
21 is a repdigit in base 4 (111).
21 is the smallest number of differently sized squares needed to square the square.