82713312 has 144 divisors (see below), whose sum is σ = 266378112. Its totient is φ = 25038720.

The previous prime is 82713299. The next prime is 82713329. The reversal of 82713312 is 21331728.

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 (27).

It is a congruent number.

It is an unprimeable number.

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 23 ways as a sum of consecutive naturals, for example, 85053 + ... + 86019.

It is an arithmetic number, because the mean of its divisors is an integer number (1849848).

Almost surely, 2^82713312 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 82713312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (133189056).

82713312 is an abundant number, since it is smaller than the sum of its proper divisors (183664800).

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

82713312 is a wasteful number, since it uses less digits than its factorization.

82713312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1003 (or 983 counting only the distinct ones).

The product of its digits is 2016, while the sum is 27.

The square root of 82713312 is about 9094.6859209101. The cubic root of 82713312 is about 435.7042575391.

The spelling of 82713312 in words is "eighty-two million, seven hundred thirteen thousand, three hundred twelve".