413189512512 has 448 divisors, whose sum is σ = 1371839938560. Its totient is φ = 107097292800.

The previous prime is 413189512441. The next prime is 413189512513. The reversal of 413189512512 is 215215981314.

It is a tau number, because it is divible by the number of its divisors (448).

It is a Harshad number since it is a multiple of its sum of digits (42).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413189512513) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 76784062 + ... + 76789442.

It is an arithmetic number, because the mean of its divisors is an integer number (3062142720).

Almost surely, 2^413189512512 is an apocalyptic number.

413189512512 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 413189512512, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (685919969280).

413189512512 is an abundant number, since it is smaller than the sum of its proper divisors (958650426048).

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

413189512512 is a wasteful number, since it uses less digits than its factorization.

413189512512 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5550 (or 5540 counting only the distinct ones).

The product of its digits is 86400, while the sum is 42.

The spelling of 413189512512 in words is "four hundred thirteen billion, one hundred eighty-nine million, five hundred twelve thousand, five hundred twelve".