3872 has 18 divisors (see below), whose sum is σ = 8379. Its totient is φ = 1760.

The previous prime is 3863. The next prime is 3877. The reversal of 3872 is 2783.

Subtracting from 3872 its reverse (2783), we obtain a square (1089 = 33^{2}).

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

3872 is an esthetic number in base 15, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in only one way, i.e., 1936 + 1936 = 44^2 + 44^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=44.

It is an Ulam number.

It is an alternating number because its digits alternate between odd and even.

It is a Duffinian number.

It is a plaindrome in base 13.

It is a nialpdrome in base 8 and base 16.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 3872.

It is not an unprimeable number, because it can be changed into a prime (3877) by changing a digit.

3872 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 2 ways as a sum of consecutive naturals, for example, 347 + ... + 357.

2^{3872} is an apocalyptic number.

3872 is a gapful number since it is divisible by the number (32) 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 3872

3872 is an abundant number, since it is smaller than the sum of its proper divisors (4507).

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

3872 is a wasteful number, since it uses less digits than its factorization.

3872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 32 (or 13 counting only the distinct ones).

The product of its digits is 336, while the sum is 20.

The square root of 3872 is about 62.2253967444. The cubic root of 3872 is about 15.7028488211.

The spelling of 3872 in words is "three thousand, eight hundred seventy-two".

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