1006538400 has 540 divisors, whose sum is σ = 4283409438. Its totient is φ = 229340160.

The previous prime is 1006538399. The next prime is 1006538419. The reversal of 1006538400 is 48356001.

1006538400 is a `hidden beast` number, since 1 + 0 + 0 + 653 + 8 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 480661776 + 525876624 = 21924^2 + 22932^2 .

It is a tau number, because it is divible by the number of its divisors (540).

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

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, 3175042 + ... + 3175358.

Almost surely, 2^1006538400 is an apocalyptic number.

1006538400 is a gapful number since it is divisible by the number (10) 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 1006538400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2141704719).

1006538400 is an abundant number, since it is smaller than the sum of its proper divisors (3276871038).

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

1006538400 is a wasteful number, since it uses less digits than its factorization.

1006538400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 363 (or 334 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 1006538400 is about 31725.9893462757. The cubic root of 1006538400 is about 1002.1747337712.

The spelling of 1006538400 in words is "one billion, six million, five hundred thirty-eight thousand, four hundred".