1006400 has 84 divisors (see below), whose sum is σ = 2692908. Its totient is φ = 368640.

The previous prime is 1006393. The next prime is 1006433. The reversal of 1006400 is 46001.

1006400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 6 ways, for example, as 53824 + 952576 = 232^2 + 976^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 27182 + ... + 27218.

2^1006400 is an apocalyptic number.

1006400 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 1006400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1346454).

1006400 is an abundant number, since it is smaller than the sum of its proper divisors (1686508).

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

1006400 is a wasteful number, since it uses less digits than its factorization.

1006400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 76 (or 61 counting only the distinct ones).

The product of its (nonzero) digits is 24, while the sum is 11.

The square root of 1006400 is about 1003.1948963188. The cubic root of 1006400 is about 100.2128798335.

It can be divided in two parts, 100 and 6400, that multiplied together give a square (640000 = 800²).

The spelling of 1006400 in words is "one million, six thousand, four hundred".