385610400 has 324 divisors, whose sum is σ = 1583207262. Its totient is φ = 88058880.

The previous prime is 385610359. The next prime is 385610417. The reversal of 385610400 is 4016583.

385610400 is a `hidden beast` number, since 3 + 8 + 5 + 610 + 40 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 370023696 + 15586704 = 19236^2 + 3948^2 .

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 352254 + ... + 353346.

Almost surely, 2^385610400 is an apocalyptic number.

385610400 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 385610400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (791603631).

385610400 is an abundant number, since it is smaller than the sum of its proper divisors (1197596862).

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

385610400 is a wasteful number, since it uses less digits than its factorization.

385610400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1133 (or 1110 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 385610400 is about 19636.9651423024. The cubic root of 385610400 is about 727.8628933120.

Adding to 385610400 its reverse (4016583), we get a palindrome (389626983).

The spelling of 385610400 in words is "three hundred eighty-five million, six hundred ten thousand, four hundred".