413629164 has 144 divisors (see below), whose sum is σ = 1196438880. Its totient is φ = 119439360.

The previous prime is 413629163. The next prime is 413629199. The reversal of 413629164 is 461926314.

413629164 is a `hidden beast` number, since 4 + 13 + 629 + 16 + 4 = 666.

It is a super-2 number, since 2×413629164² = 342178170622677792, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a nude number because it is divisible by every one of its digits.

It is not an unprimeable number, because it can be changed into a prime (413629163) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1609324 + ... + 1609580.

Almost surely, 2^413629164 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413629164, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (598219440).

413629164 is an abundant number, since it is smaller than the sum of its proper divisors (782809716).

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

413629164 is a wasteful number, since it uses less digits than its factorization.

413629164 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 480 (or 475 counting only the distinct ones).

The product of its digits is 31104, while the sum is 36.

The square root of 413629164 is about 20337.8751102469. The cubic root of 413629164 is about 745.0813922456.

The spelling of 413629164 in words is "four hundred thirteen million, six hundred twenty-nine thousand, one hundred sixty-four".