38401 has 4 divisors (see below), whose sum is σ = 41904. Its totient is φ = 34900.

The previous prime is 38393. The next prime is 38431. The reversal of 38401 is 10483.

38401 = T₇₈ + T₇₉ + ... + T₈₈.

38401 = 54² + 55² + ... + 64².

It is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4, and also an emirpimes, since its reverse is a distinct semiprime: 10483 = 11 ⋅953.

It is a cyclic number.

It is not a de Polignac number, because 38401 - 2³ = 38393 is a prime.

It is a Duffinian number.

38401 is a lucky number.

It is not an unprimeable number, because it can be changed into a prime (38431) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1735 + ... + 1756.

It is an arithmetic number, because the mean of its divisors is an integer number (10476).

It is a Proth number, since it is equal to 75 ⋅ 2⁹ + 1 and 75 < 2⁹.

2³⁸⁴⁰¹ is an apocalyptic number.

It is an amenable number.

38401 is a deficient number, since it is larger than the sum of its proper divisors (3503).

38401 is a wasteful number, since it uses less digits than its factorization.

38401 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3502.

The product of its (nonzero) digits is 96, while the sum is 16.

The square root of 38401 is about 195.9617309579. The cubic root of 38401 is about 33.7375994681.

Multiplying 38401 by its sum of digits (16), we get a palindrome (614416).

Adding to 38401 its reverse (10483), we get a palindrome (48884).

The spelling of 38401 in words is "thirty-eight thousand, four hundred one".