413046144 has 384 divisors, whose sum is σ = 1512276480. Its totient is φ = 105431040.

The previous prime is 413046131. The next prime is 413046173. The reversal of 413046144 is 441640314.

413046144 is a `hidden beast` number, since 41 + 3 + 0 + 4 + 614 + 4 = 666.

It is a tau number, because it is divible by the number of its divisors (384).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3152959 + ... + 3153089.

It is an arithmetic number, because the mean of its divisors is an integer number (3938220).

Almost surely, 2^413046144 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 413046144, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (756138240).

413046144 is an abundant number, since it is smaller than the sum of its proper divisors (1099230336).

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

413046144 is a wasteful number, since it uses less digits than its factorization.

413046144 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 198 (or 183 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 27.

The square root of 413046144 is about 20323.5367000923. The cubic root of 413046144 is about 744.7311577450.

Adding to 413046144 its reverse (441640314), we get a palindrome (854686458).

The spelling of 413046144 in words is "four hundred thirteen million, forty-six thousand, one hundred forty-four".