820512 has 144 divisors (see below), whose sum is σ = 2987712. Its totient is φ = 207360.

The previous prime is 820489. The next prime is 820537. The reversal of 820512 is 215028.

It is a tau number, because it is divible by the number of its divisors (144).

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

It is a nialpdrome in base 7 and base 16.

It is an unprimeable number.

820512 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 22158 + ... + 22194.

It is an arithmetic number, because the mean of its divisors is an integer number (20748).

2⁸²⁰⁵¹² 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 820512, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1493856).

820512 is an abundant number, since it is smaller than the sum of its proper divisors (2167200).

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

820512 is a wasteful number, since it uses less digits than its factorization.

820512 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 71 (or 60 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

The square root of 820512 is about 905.8211744047. The cubic root of 820512 is about 93.6184929491.

The spelling of 820512 in words is "eight hundred twenty thousand, five hundred twelve".