413505120 has 144 divisors (see below), whose sum is σ = 1515287088. Its totient is φ = 94510080.

The previous prime is 413505101. The next prime is 413505121. The reversal of 413505120 is 21505314.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413505121) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 14730 + ... + 32310.

It is an arithmetic number, because the mean of its divisors is an integer number (10522827).

Almost surely, 2^413505120 is an apocalyptic number.

413505120 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413505120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (757643544).

413505120 is an abundant number, since it is smaller than the sum of its proper divisors (1101781968).

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

413505120 is a wasteful number, since it uses less digits than its factorization.

413505120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 17613 (or 17598 counting only the distinct ones).

The product of its (nonzero) digits is 600, while the sum is 21.

The square root of 413505120 is about 20334.8253004544. The cubic root of 413505120 is about 745.0069035290.

The spelling of 413505120 in words is "four hundred thirteen million, five hundred five thousand, one hundred twenty".