413019813888 has 768 divisors, whose sum is σ = 1380983385600. Its totient is φ = 122425344000.

The previous prime is 413019813883. The next prime is 413019813919. The reversal of 413019813888 is 888318910314.

413019813888 is a `hidden beast` number, since 41 + 30 + 198 + 1 + 388 + 8 = 666.

It is a tau number, because it is divible by the number of its divisors (768).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413019813883) 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, 4089305038 + ... + 4089305138.

It is an arithmetic number, because the mean of its divisors is an integer number (1798155450).

Almost surely, 2^413019813888 is an apocalyptic number.

413019813888 is a gapful number since it is divisible by the number (48) 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 413019813888, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (690491692800).

413019813888 is an abundant number, since it is smaller than the sum of its proper divisors (967963571712).

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

413019813888 is an equidigital number, since it uses as much as digits as its factorization.

413019813888 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 238 (or 200 counting only the distinct ones).

The product of its (nonzero) digits is 1327104, while the sum is 54.

The spelling of 413019813888 in words is "four hundred thirteen billion, nineteen million, eight hundred thirteen thousand, eight hundred eighty-eight".