413401234000 has 80 divisors (see below), whose sum is σ = 1008450789840. Its totient is φ = 163897036800.

The previous prime is 413401233991. The next prime is 413401234009. The reversal of 413401234000 is 432104314.

It is an interprime number because it is at equal distance from previous prime (413401233991) and next prime (413401234009).

It can be written as a sum of positive squares in 8 ways, for example, as 315134031424 + 98267202576 = 561368^2 + 313476^2 .

It is a tau number, because it is divible by the number of its divisors (80).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413401234009) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 688605 + ... + 1140604.

It is an arithmetic number, because the mean of its divisors is an integer number (12605634873).

Almost surely, 2^413401234000 is an apocalyptic number.

413401234000 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

413401234000 is an abundant number, since it is smaller than the sum of its proper divisors (595049555840).

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

413401234000 is a wasteful number, since it uses less digits than its factorization.

413401234000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1829345 (or 1829329 counting only the distinct ones).

The product of its (nonzero) digits is 1152, while the sum is 22.

Adding to 413401234000 its reverse (432104314), we get a palindrome (413833338314).

The spelling of 413401234000 in words is "four hundred thirteen billion, four hundred one million, two hundred thirty-four thousand".