413022600 has 144 divisors (see below), whose sum is σ = 1393856100. Its totient is φ = 109601280.

The previous prime is 413022541. The next prime is 413022607. The reversal of 413022600 is 6220314.

It is a happy number.

413022600 is a `hidden beast` number, since 41 + 3 + 0 + 22 + 600 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 4901796 + 408120804 = 2214^2 + 20202^2 .

It is a super-2 number, since 2×413022600² = 341175336221520000, which contains 22 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (413022607) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 483774 + ... + 484626.

Almost surely, 2^413022600 is an apocalyptic number.

413022600 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 413022600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (696928050).

413022600 is an abundant number, since it is smaller than the sum of its proper divisors (980833500).

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

413022600 is a wasteful number, since it uses less digits than its factorization.

413022600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1144 (or 1132 counting only the distinct ones).

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

The square root of 413022600 is about 20322.9574619444. The cubic root of 413022600 is about 744.7170073619.

Adding to 413022600 its reverse (6220314), we get a palindrome (419242914).

The spelling of 413022600 in words is "four hundred thirteen million, twenty-two thousand, six hundred".