413404041232000 has 768 divisors, whose sum is σ = 1288794170270880. Its totient is φ = 130714833715200.

The previous prime is 413404041231977. The next prime is 413404041232027. The reversal of 413404041232000 is 232140404314.

It can be written as a sum of positive squares in 16 ways, for example, as 255564217613376 + 157839823618624 = 15986376^2 + 12563432^2 .

It is a Harshad number since it is a multiple of its sum of digits (28).

It is a self number, because there is not a number n which added to its sum of digits gives 413404041232000.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 11384445844 + ... + 11384482156.

Almost surely, 2^{413404041232000} is an apocalyptic number.

413404041232000 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 413404041232000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (644397085135440).

413404041232000 is an abundant number, since it is smaller than the sum of its proper divisors (875390129038880).

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

413404041232000 is a wasteful number, since it uses less digits than its factorization.

413404041232000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 37486 (or 37457 counting only the distinct ones).

The product of its (nonzero) digits is 9216, while the sum is 28.

Adding to 413404041232000 its reverse (232140404314), we get a palindrome (413636181636314).

The spelling of 413404041232000 in words is "four hundred thirteen trillion, four hundred four billion, forty-one million, two hundred thirty-two thousand".