413406 has 48 divisors (see below), whose sum is σ = 1089504. Its totient is φ = 110592.

The previous prime is 413353. The next prime is 413411. The reversal of 413406 is 604314.

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

It is a nialpdrome in base 14.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2046 + ... + 2238.

It is an arithmetic number, because the mean of its divisors is an integer number (22698).

2⁴¹³⁴⁰⁶ is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413406, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (544752).

413406 is an abundant number, since it is smaller than the sum of its proper divisors (676098).

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

413406 is a wasteful number, since it uses less digits than its factorization.

413406 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 225 (or 222 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 18.

The square root of 413406 is about 642.9665621166. The cubic root of 413406 is about 74.4947371025.

The spelling of 413406 in words is "four hundred thirteen thousand, four hundred six".