1585440864 has 504 divisors, whose sum is σ = 5808945240. Its totient is φ = 423263232.

The previous prime is 1585440833. The next prime is 1585440869. The reversal of 1585440864 is 4680445851.

It is a happy number.

1585440864 is a `hidden beast` number, since 1 + 585 + 4 + 4 + 0 + 8 + 64 = 666.

It is a tau number, because it is divible by the number of its divisors (504).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1585440869) by changing a digit.

It is a polite number, since it can be written in 83 ways as a sum of consecutive naturals, for example, 21718332 + ... + 21718404.

It is an arithmetic number, because the mean of its divisors is an integer number (11525685).

Almost surely, 2^1585440864 is an apocalyptic number.

1585440864 is a gapful number since it is divisible by the number (14) 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 1585440864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2904472620).

1585440864 is an abundant number, since it is smaller than the sum of its proper divisors (4223504376).

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

1585440864 is an equidigital number, since it uses as much as digits as its factorization.

1585440864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 134 (or 104 counting only the distinct ones).

The product of its (nonzero) digits is 614400, while the sum is 45.

The square root of 1585440864 is about 39817.5949047654. The cubic root of 1585440864 is about 1166.0486824889.

The spelling of 1585440864 in words is "one billion, five hundred eighty-five million, four hundred forty thousand, eight hundred sixty-four".