395413200 has 720 divisors, whose sum is σ = 1813383936. Its totient is φ = 77414400.

The previous prime is 395413159. The next prime is 395413201. The reversal of 395413200 is 2314593.

It is a tau number, because it is divible by the number of its divisors (720).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (395413201) 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 143 ways as a sum of consecutive naturals, for example, 5569165 + ... + 5569235.

Almost surely, 2^395413200 is an apocalyptic number.

395413200 is a gapful number since it is divisible by the number (30) 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 395413200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (906691968).

395413200 is an abundant number, since it is smaller than the sum of its proper divisors (1417970736).

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

395413200 is a wasteful number, since it uses less digits than its factorization.

395413200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 132 (or 118 counting only the distinct ones).

The product of its (nonzero) digits is 3240, while the sum is 27.

The square root of 395413200 is about 19884.9993713855. Note that the first 3 decimals coincide. The cubic root of 395413200 is about 733.9791464302.

Adding to 395413200 its reverse (2314593), we get a palindrome (397727793).

It can be divided in two parts, 395 and 413200, that added together give a triangular number (413595 = T₉₀₉).

The spelling of 395413200 in words is "three hundred ninety-five million, four hundred thirteen thousand, two hundred".