400

Number
$400$ (four hundred) is:


 * $2^4 \times 5^2$


 * The $20$th square number after $1, 4, 9, 16, 25, 36, \ldots, 225, 256, 289, 324, 361$:
 * $400 = 20 \times 20$


 * The $24$th number, and $3$rd square number after $1, 81$, whose $\sigma$ value is square:


 * The $\sigma$ value of $7^3$, and so:
 * $400 = 20^2 = 7^0 + 7^1 + 7^2 + 7^3$


 * The $6$th even integer after $2, 4, 94, 96, 98$ that cannot be expressed as the sum of $2$ prime numbers which are each one of a pair of twin primes.


 * The $18$th positive integer after $64, 96, 128, 144, \ldots, 320, 324, 336, 352, 360, 384$ with $6$ or more prime factors:
 * $400 = 2 \times 2 \times 2 \times 2 \times 5 \times 5$


 * The $18$th positive integer which cannot be expressed as the sum of a square and a prime:
 * $1, 10, 25, 34, 58, 64, 85, 91, 121, 130, 169, 196, 214, 226, 289, 324, 370, 400, \ldots$

Also see

 * Sigma of 343