385169184400 has 1215 divisors, whose sum is σ = 1323884881179. Its totient is φ = 107243136000.

The previous prime is 385169184373. The next prime is 385169184443. The reversal of 385169184400 is 4481961583.

It is a happy number.

The square root of 385169184400 is 620620.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 4 ways, for example, as 99277927056 + 285891257344 = 315084^2 + 534688^2 .

It is a super-2 number, since 2×385169184400² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (49).

It is an unprimeable number.

It is a polite number, since it can be written in 242 ways as a sum of consecutive naturals, for example, 12424812385 + ... + 12424812415.

Almost surely, 2^385169184400 is an apocalyptic number.

385169184400 is the 620620-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 385169184400

385169184400 is an abundant number, since it is smaller than the sum of its proper divisors (938715696779).

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

385169184400 is a wasteful number, since it uses less digits than its factorization.

385169184400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 142 (or 69 counting only the distinct ones).

The product of its (nonzero) digits is 829440, while the sum is 49.

Multiplying 385169184400 by its sum of digits (49), we get a square (18873290035600 = 4344340²).

385169184400 divided by its sum of digits (49) gives a square (7860595600 = 88660²).

The spelling of 385169184400 in words is "three hundred eighty-five billion, one hundred sixty-nine million, one hundred eighty-four thousand, four hundred".