1038128400 has 225 divisors, whose sum is σ = 3746690101. Its totient is φ = 275287680.

The previous prime is 1038128389. The next prime is 1038128411. The reversal of 1038128400 is 48218301.

The square root of 1038128400 is 32220.

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

1038128400 is a `hidden beast` number, since 1 + 0 + 381 + 284 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (1038128389) and next prime (1038128411).

It can be written as a sum of positive squares in only one way, i.e., 373726224 + 664402176 = 19332^2 + 25776^2 .

It is a tau number, because it is divible by the number of its divisors (225).

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

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 5799511 + ... + 5799689.

Almost surely, 2^1038128400 is an apocalyptic number.

1038128400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

1038128400 is the 32220-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1038128400

1038128400 is an abundant number, since it is smaller than the sum of its proper divisors (2708561701).

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

1038128400 is an equidigital number, since it uses as much as digits as its factorization.

1038128400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 388 (or 189 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 27.

The cubic root of 1038128400 is about 1012.5512731236.

It can be divided in two parts, 10381 and 28400, that added together give a triangular number (38781 = T₂₇₈).

The spelling of 1038128400 in words is "one billion, thirty-eight million, one hundred twenty-eight thousand, four hundred".