413813400 has 576 divisors, whose sum is σ = 1764529920. Its totient is φ = 77875200.

The previous prime is 413813399. The next prime is 413813417. The reversal of 413813400 is 4318314.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 7807774 + ... + 7807826.

It is an arithmetic number, because the mean of its divisors is an integer number (3063420).

Almost surely, 2^413813400 is an apocalyptic number.

413813400 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 413813400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (882264960).

413813400 is an abundant number, since it is smaller than the sum of its proper divisors (1350716520).

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

413813400 is a wasteful number, since it uses less digits than its factorization.

413813400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 116 (or 94 counting only the distinct ones).

The product of its (nonzero) digits is 1152, while the sum is 24.

The square root of 413813400 is about 20342.4039877297. The cubic root of 413813400 is about 745.1919989207.

The spelling of 413813400 in words is "four hundred thirteen million, eight hundred thirteen thousand, four hundred".