3681

3681 is a positive integer that sits between 3680 and 3682. It is a composite number with prime factorization 3^2 × 409, where 409 is a prime number.

Its six positive divisors are 1, 3, 9, 409, 1227, and 3681. This reflects its factorization as 3^2 times 409, giving a divisor count of (2+1)(1+1) = 6.

In number theory, 3681 can be expressed as a sum of two squares: 3681 = 9^2 + 60^2. This aligns with its prime factorization, since 409 is congruent to 1 modulo 4 and thus expressible as a sum of two squares; combining with 3^2 preserves this property.

Representations in different bases include binary 111001100001, octal 7141, and hexadecimal E61. In Roman numerals, 3681 is written as MMMDCLXXXI.

As a decimal integer, 3681 is also commonly used as a simple example in discussions of factorization, divisors, and representations as sums of squares. It illustrates how a number with a square factor and a prime component of the form 4k+1 can yield a sum-of-squares representation.