81585000 has 360 divisors, whose sum is σ = 329870970. Its totient is φ = 18144000.

The previous prime is 81584981. The next prime is 81585013. The reversal of 81585000 is 58518.

81585000 is a `hidden beast` number, since 8 + 158 + 500 + 0 = 666.

It can be written as a sum of positive squares in 5 ways, for example, as 8892324 + 72692676 = 2982^2 + 8526^2 .

It is a tau number, because it is divible by the number of its divisors (360).

It is a super-2 number, since 2×81585000² = 13312224450000000, which contains 22 as substring.

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is an unprimeable number.

It is a polite number, since it can be written in 89 ways as a sum of consecutive naturals, for example, 2204982 + ... + 2205018.

Almost surely, 2^81585000 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 81585000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (164935485).

81585000 is an abundant number, since it is smaller than the sum of its proper divisors (248285970).

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

81585000 is a wasteful number, since it uses less digits than its factorization.

81585000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 83 (or 54 counting only the distinct ones).

The product of its (nonzero) digits is 1600, while the sum is 27.

The square root of 81585000 is about 9032.4415303948. The cubic root of 81585000 is about 433.7139981801.

The spelling of 81585000 in words is "eighty-one million, five hundred eighty-five thousand".