413484134400 has 1092 divisors, whose sum is σ = 1598605361280. Its totient is φ = 105902899200.

The previous prime is 413484134383. The next prime is 413484134411. The reversal of 413484134400 is 4431484314.

413484134400 is a `hidden beast` number, since 4 + 1 + 3 + 484 + 134 + 40 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 83 ways as a sum of consecutive naturals, for example, 2164838305 + ... + 2164838495.

Almost surely, 2^413484134400 is an apocalyptic number.

413484134400 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 413484134400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (799302680640).

413484134400 is an abundant number, since it is smaller than the sum of its proper divisors (1185121226880).

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

413484134400 is an equidigital number, since it uses as much as digits as its factorization.

413484134400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 272 (or 230 counting only the distinct ones).

The product of its (nonzero) digits is 73728, while the sum is 36.

The spelling of 413484134400 in words is "four hundred thirteen billion, four hundred eighty-four million, one hundred thirty-four thousand, four hundred".