82534400 has 168 divisors, whose sum is σ = 227527104. Its totient is φ = 29491200.

The previous prime is 82534399. The next prime is 82534421. The reversal of 82534400 is 443528.

It is a Harshad number since it is a multiple of its sum of digits (26).

It is a self number, because there is not a number n which added to its sum of digits gives 82534400.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2662385 + ... + 2662415.

It is an arithmetic number, because the mean of its divisors is an integer number (1354328).

Almost surely, 2^82534400 is an apocalyptic number.

82534400 is a gapful number since it is divisible by the number (80) 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 82534400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (113763552).

82534400 is an abundant number, since it is smaller than the sum of its proper divisors (144992704).

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

82534400 is a wasteful number, since it uses less digits than its factorization.

82534400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 80 (or 51 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 26.

The square root of 82534400 is about 9084.8445226102. The cubic root of 82534400 is about 435.3898825380.

Adding to 82534400 its reverse (443528), we get a palindrome (82977928).

The spelling of 82534400 in words is "eighty-two million, five hundred thirty-four thousand, four hundred".