413088 has 48 divisors (see below), whose sum is σ = 1171296. Its totient is φ = 126720.

The previous prime is 413087. The next prime is 413089. The reversal of 413088 is 880314.

It is an interprime number because it is at equal distance from previous prime (413087) and next prime (413089).

It is a tau number, because it is divible by the number of its divisors (48).

It is a Smith number, since the sum of its digits (24) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is not an unprimeable number, because it can be changed into a prime (413081) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1083 + ... + 1413.

It is an arithmetic number, because the mean of its divisors is an integer number (24402).

2⁴¹³⁰⁸⁸ is an apocalyptic number.

413088 is a gapful number since it is divisible by the number (48) 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 413088, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (585648).

413088 is an abundant number, since it is smaller than the sum of its proper divisors (758208).

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

413088 is a wasteful number, since it uses less digits than its factorization.

413088 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 357 (or 349 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 24.

The square root of 413088 is about 642.7192233005. The cubic root of 413088 is about 74.4756312654.

The spelling of 413088 in words is "four hundred thirteen thousand, eighty-eight".