638401 has 9 divisors (see below), whose sum is σ = 692899. Its totient is φ = 588064.

The previous prime is 638371. The next prime is 638423. The reversal of 638401 is 104836.

The square root of 638401 is 799.

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

It can be written as a sum of positive squares in only one way, i.e., 497025 + 141376 = 705^2 + 376^2 .

It is not a de Polignac number, because 638401 - 2¹¹ = 636353 is a prime.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (638431) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 13560 + ... + 13606.

2⁶³⁸⁴⁰¹ is an apocalyptic number.

638401 is the 799-th square number.

638401 is the 400-th centered octagonal number.

It is an amenable number.

638401 is a deficient number, since it is larger than the sum of its proper divisors (54498).

638401 is an equidigital number, since it uses as much as digits as its factorization.

638401 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 128 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 22.

The cubic root of 638401 is about 86.1055581419.

Multiplying 638401 by its product of nonzero digits (576), we get a square (367718976 = 19176²).

It can be divided in two parts, 63 and 8401, that added together give a square (8464 = 92²).

The spelling of 638401 in words is "six hundred thirty-eight thousand, four hundred one".