4200013004400 has 300 divisors, whose sum is σ = 15078180526200. Its totient is φ = 1119656424960.

The previous prime is 4200013004393. The next prime is 4200013004471. The reversal of 4200013004400 is 44003100024.

4200013004400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (300).

It is a super-2 number, since 2×4200013004400² (a number of 26 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 114645286 + ... + 114681914.

It is an arithmetic number, because the mean of its divisors is an integer number (50260601754).

Almost surely, 2^{4200013004400} is an apocalyptic number.

4200013004400 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 4200013004400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7539090263100).

4200013004400 is an abundant number, since it is smaller than the sum of its proper divisors (10878167521800).

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

4200013004400 is a wasteful number, since it uses less digits than its factorization.

4200013004400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 40198 (or 40178 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 18.

Adding to 4200013004400 its reverse (44003100024), we get a palindrome (4244016104424).

The spelling of 4200013004400 in words is "four trillion, two hundred billion, thirteen million, four thousand, four hundred".