413504 has 56 divisors (see below), whose sum is σ = 1024128. Its totient is φ = 161280.

The previous prime is 413477. The next prime is 413521. The reversal of 413504 is 405314.

It is a tau number, because it is divible by the number of its divisors (56).

It is a congruent number.

It is an unprimeable number.

413504 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 5789 + ... + 5859.

It is an arithmetic number, because the mean of its divisors is an integer number (18288).

2⁴¹³⁵⁰⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413504, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (512064).

413504 is an abundant number, since it is smaller than the sum of its proper divisors (610624).

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

413504 is a wasteful number, since it uses less digits than its factorization.

413504 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 103 (or 93 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 17.

The square root of 413504 is about 643.0427668515. The cubic root of 413504 is about 74.5006230898.

Adding to 413504 its reverse (405314), we get a palindrome (818818).

The spelling of 413504 in words is "four hundred thirteen thousand, five hundred four".