34816000 has 120 divisors (see below), whose sum is σ = 92009736. Its totient is φ = 13107200.

The previous prime is 34815971. The next prime is 34816021. The reversal of 34816000 is 61843.

It can be written as a sum of positive squares in 4 ways, for example, as 147456 + 34668544 = 384^2 + 5888^2 .

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2047992 + ... + 2048008.

Almost surely, 2^34816000 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 34816000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (46004868).

34816000 is an abundant number, since it is smaller than the sum of its proper divisors (57193736).

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

34816000 is an frugal number, since it uses more digits than its factorization.

34816000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 60 (or 24 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 22.

The square root of 34816000 is about 5900.5084526674. The cubic root of 34816000 is about 326.5324081534.

Adding to 34816000 its reverse (61843), we get a palindrome (34877843).

It can be divided in two parts, 3 and 4816000, that multiplied together give a triangular number (14448000 = T₅₃₇₅).

The spelling of 34816000 in words is "thirty-four million, eight hundred sixteen thousand".