81285120 has 390 divisors, whose sum is σ = 338959962. Its totient is φ = 18579456.

The previous prime is 81285101. The next prime is 81285121. The reversal of 81285120 is 2158218.

It can be written as a sum of positive squares in only one way, i.e., 65028096 + 16257024 = 8064^2 + 4032^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (81285121) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 11612157 + ... + 11612163.

Almost surely, 2^81285120 is an apocalyptic number.

81285120 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 81285120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (169479981).

81285120 is an abundant number, since it is smaller than the sum of its proper divisors (257674842).

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

81285120 is an equidigital number, since it uses as much as digits as its factorization.

81285120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 55 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 1280, while the sum is 27.

The square root of 81285120 is about 9015.8260852792. The cubic root of 81285120 is about 433.1819484348.

Multiplying 81285120 by its product of nonzero digits (1280), we get a square (104044953600 = 322560²).

81285120 divided by its product of nonzero digits (1280) gives a square (63504 = 252²).

The spelling of 81285120 in words is "eighty-one million, two hundred eighty-five thousand, one hundred twenty".