405306 has 48 divisors (see below), whose sum is σ = 1010880. Its totient is φ = 116160.

The previous prime is 405299. The next prime is 405323. The reversal of 405306 is 603504.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

405306 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 4510 + ... + 4598.

It is an arithmetic number, because the mean of its divisors is an integer number (21060).

2⁴⁰⁵³⁰⁶ is an apocalyptic number.

405306 is a gapful number since it is divisible by the number (46) formed by its first and last digit.

It is a practical number, because each smaller number is the sum of distinct divisors of 405306, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (505440).

405306 is an abundant number, since it is smaller than the sum of its proper divisors (605574).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

405306 is a wasteful number, since it uses less digits than its factorization.

405306 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 131 (or 128 counting only the distinct ones).

The product of its (nonzero) digits is 360, while the sum is 18.

The square root of 405306 is about 636.6364739787. The cubic root of 405306 is about 74.0049911413.

The spelling of 405306 in words is "four hundred five thousand, three hundred six".