413021320002 has 112 divisors (see below), whose sum is σ = 936368684280. Its totient is φ = 136566590976.

The previous prime is 413021319989. The next prime is 413021320109. The reversal of 413021320002 is 200023120314.

413021320002 is a `hidden beast` number, since 41 + 302 + 1 + 320 + 0 + 0 + 2 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 387756535401 + 25264784601 = 622701^2 + 158949^2 .

It is a super-2 number, since 2×413021320002² (a number of 24 digits) contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 55 ways as a sum of consecutive naturals, for example, 128385498 + ... + 128388714.

Almost surely, 2^413021320002 is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413021320002, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (468184342140).

413021320002 is an abundant number, since it is smaller than the sum of its proper divisors (523347364278).

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

413021320002 is a wasteful number, since it uses less digits than its factorization.

413021320002 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3919 (or 3904 counting only the distinct ones).

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

Adding to 413021320002 its reverse (200023120314), we get a palindrome (613044440316).

The spelling of 413021320002 in words is "four hundred thirteen billion, twenty-one million, three hundred twenty thousand, two".