In Mathematics
Twenty-one is the fifth discrete Semiprime and the second in the (3.q) family. With 22 it forms the second discrete Semiprime pair. As it is a semiprime with both its prime factors being Gaussian primes, 21 is then a Blum integer.
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, its proper divisors being 1, 3 and 7.
21 is the sum of the first six natural numbers (1+2+3+4+5+6=21).
21 has an aliquot sum of 11 though it is the second composite number found in the 11-aliquot tree with the abundant square prime 18 being the first such member. Twenty-one is the first number to be the aliquot sum of three numbers 18, 51, 91.
21 appears in the Padovan sequence, preceded by the terms 9, 12, 16 (it is the sum of the first two of these).
The sum of divisors for the integers 1 through 6 is 21.
21 is the smallest non-trivial example of a Fibonacci number whose digits are Fibonacci numbers and whose digit sum is also a Fibonacci number.
21 is a repdigit in base 4 (111).
21 is the smallest natural number that is not close to a power of 2, 2^n, where the range of closeness is +- n.
21 is the smallest number of differently sized squares needed to square the square.
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