413042020820 has 288 divisors, whose sum is σ = 1116582322464. Its totient is φ = 126955192320.

The previous prime is 413042020819. The next prime is 413042020823. The reversal of 413042020820 is 28020240314.

It can be written as a sum of positive squares in 16 ways, for example, as 54906799684 + 358135221136 = 234322^2 + 598444^2 .

It is a Harshad number since it is a multiple of its sum of digits (26).

It is a self number, because there is not a number n which added to its sum of digits gives 413042020820.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413042020823) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 19777904 + ... + 19798776.

It is an arithmetic number, because the mean of its divisors is an integer number (3877021953).

Almost surely, 2^413042020820 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 413042020820, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (558291161232).

413042020820 is an abundant number, since it is smaller than the sum of its proper divisors (703540301644).

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

413042020820 is a wasteful number, since it uses less digits than its factorization.

413042020820 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 20971 (or 20958 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 26.

The spelling of 413042020820 in words is "four hundred thirteen billion, forty-two million, twenty thousand, eight hundred twenty".