1005712133904 has 225 divisors, whose sum is σ = 2953331518863. Its totient is φ = 330411654144.

The previous prime is 1005712133893. The next prime is 1005712133917. The reversal of 1005712133904 is 4093312175001.

The square root of 1005712133904 is 1002852.

It is a perfect power (a square), and thus also a powerful number.

1005712133904 is a `hidden beast` number, since 1 + 0 + 0 + 57 + 1 + 213 + 390 + 4 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 745563171600 + 260148962304 = 863460^2 + 510048^2 .

It is a super-2 number, since 2×1005712133904² (a number of 25 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 3213137652 + ... + 3213137964.

Almost surely, 2^{1005712133904} is an apocalyptic number.

1005712133904 is the 1002852-nd square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1005712133904

1005712133904 is an abundant number, since it is smaller than the sum of its proper divisors (1947619384959).

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

1005712133904 is an frugal number, since it uses more digits than its factorization.

1005712133904 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 824 (or 407 counting only the distinct ones).

The product of its (nonzero) digits is 22680, while the sum is 36.

Multiplying 1005712133904 by its sum of digits (36), we get a square (36205636820544 = 6017112²).

1005712133904 divided by its sum of digits (36) gives a square (27936448164 = 167142²).

The spelling of 1005712133904 in words is "one trillion, five billion, seven hundred twelve million, one hundred thirty-three thousand, nine hundred four".