38416 has 25 divisors (see below), whose sum is σ = 86831. Its totient is φ = 16464.

The previous prime is 38393. The next prime is 38431. The reversal of 38416 is 61483.

Multipling 38416 by its product of digits (576), we get a square (22127616 = 4704^{2}).

Adding to 38416 its reverse (61483), we get a palindrome (99899).

It can be divided in two parts, 384 and 16, that added together give a square (400 = 20^{2}).

38416 = T_{195} + T_{196}.

The square root of 38416 is 196.

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

38416 is nontrivially palindromic in base 13.

It is a Duffinian number.

Its product of digits (576) is a multiple of the sum of its prime divisors (9).

It is a nialpdrome in base 7, base 14 and base 16.

It is a zygodrome in base 7.

It is an unprimeable number.

38416 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 4 ways as a sum of consecutive naturals, for example, 5485 + ... + 5491.

38416 is a Friedman number, since it can be written as (8+6)^4*1^3, using all its digits and the basic arithmetic operations.

2^{38416} is an apocalyptic number.

38416 is the 196-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 38416

38416 is an abundant number, since it is smaller than the sum of its proper divisors (48415).

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

38416 is an frugal number, since it uses more digits than its factorization.

38416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 36 (or 9 counting only the distinct ones).

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

The cubic root of 38416 is about 33.7419916985.

The spelling of 38416 in words is "thirty-eight thousand, four hundred sixteen".

Divisors: 1 2 4 7 8 14 16 28 49 56 98 112 196 343 392 686 784 1372 2401 2744 4802 5488 9604 19208 38416

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