413213000 has 64 divisors (see below), whose sum is σ = 972382320. Its totient is φ = 164352000.

The previous prime is 413212997. The next prime is 413213011. The reversal of 413213000 is 312314.

It can be written as a sum of positive squares in 8 ways, for example, as 43112356 + 370100644 = 6566^2 + 19238^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 191930 + ... + 194070.

Almost surely, 2^413213000 is an apocalyptic number.

413213000 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 413213000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (486191160).

413213000 is an abundant number, since it is smaller than the sum of its proper divisors (559169320).

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

413213000 is a wasteful number, since it uses less digits than its factorization.

413213000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2355 (or 2341 counting only the distinct ones).

The product of its (nonzero) digits is 72, while the sum is 14.

The square root of 413213000 is about 20327.6412797944. The cubic root of 413213000 is about 744.8314259071.

Adding to 413213000 its reverse (312314), we get a palindrome (413525314).

The spelling of 413213000 in words is "four hundred thirteen million, two hundred thirteen thousand".