413075400192 has 960 divisors, whose sum is σ = 1558909598400. Its totient is φ = 107017666560.

The previous prime is 413075400187. The next prime is 413075400197. The reversal of 413075400192 is 291004570314.

413075400192 is a `hidden beast` number, since 413 + 0 + 7 + 54 + 0 + 0 + 192 = 666.

It is an interprime number because it is at equal distance from previous prime (413075400187) and next prime (413075400197).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413075400197) 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, 537158784 + ... + 537159552.

It is an arithmetic number, because the mean of its divisors is an integer number (1623864165).

Almost surely, 2^413075400192 is an apocalyptic number.

413075400192 is a gapful number since it is divisible by the number (42) 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 413075400192, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (779454799200).

413075400192 is an abundant number, since it is smaller than the sum of its proper divisors (1145834198208).

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

413075400192 is a wasteful number, since it uses less digits than its factorization.

413075400192 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 884 (or 855 counting only the distinct ones).

The product of its (nonzero) digits is 30240, while the sum is 36.

The spelling of 413075400192 in words is "four hundred thirteen billion, seventy-five million, four hundred thousand, one hundred ninety-two".