413001100314 has 72 divisors (see below), whose sum is σ = 984275472180. Its totient is φ = 125063326080.

The previous prime is 413001100283. The next prime is 413001100321.

413001100314 is a `hidden beast` number, since 41 + 300 + 1 + 10 + 0 + 314 = 666.

413001100314 is nontrivially palindromic in base 10.

It can be written as a sum of positive squares in 2 ways, for example, as 270105760089 + 142895340225 = 519717^2 + 378015^2 .

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 35 ways as a sum of consecutive naturals, for example, 3046014 + ... + 3178710.

Almost surely, 2^413001100314 is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413001100314, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (492137736090).

413001100314 is an abundant number, since it is smaller than the sum of its proper divisors (571274371866).

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

413001100314 is a wasteful number, since it uses less digits than its factorization.

413001100314 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 134156 (or 134142 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

It can be divided in two parts, 413001 and 100314, that added together give a palindrome (513315).

The spelling of 413001100314 in words is "four hundred thirteen billion, one million, one hundred thousand, three hundred fourteen".