413512000 has 224 divisors, whose sum is σ = 1156386816. Its totient is φ = 145152000.

The previous prime is 413511997. The next prime is 413512003. The reversal of 413512000 is 215314.

It is an interprime number because it is at equal distance from previous prime (413511997) and next prime (413512003).

It is a Harshad number since it is a multiple of its sum of digits (16).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413512003) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 3255937 + ... + 3256063.

Almost surely, 2^413512000 is an apocalyptic number.

413512000 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 413512000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (578193408).

413512000 is an abundant number, since it is smaller than the sum of its proper divisors (742874816).

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

413512000 is a wasteful number, since it uses less digits than its factorization.

413512000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 202 (or 182 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 16.

The square root of 413512000 is about 20334.9944676658. The cubic root of 413512000 is about 745.0110353755.

Adding to 413512000 its reverse (215314), we get a palindrome (413727314).

The spelling of 413512000 in words is "four hundred thirteen million, five hundred twelve thousand".