3×5×7×31

3×5×7×31 is the product of four primes, namely 3, 5, 7 and 31. It equals 3255. As a product of distinct primes, the number is square-free and has 16 positive divisors.

The divisors are: 1, 3, 5, 7, 15, 21, 31, 35, 93, 105, 155, 217, 465, 651, 1085, 3255. Each divisor corresponds to a product of a subset of the prime factors.

The sum of its positive divisors, denoted sigma(n), is 6144. For a square-free number with prime factors p1, p2, p3, p4, sigma(n) = (1+p1)(1+p2)(1+p3)(1+p4), which in this case is (1+3)(1+5)(1+7)(1+31) = 4×6×8×32 = 6144.

Euler’s totient function phi(n) for a product of distinct primes equals the product of (p_i − 1). Therefore phi(3255) = (3−1)(5−1)(7−1)(31−1) = 2×4×6×30 = 1440.

The number is odd and composite. Among its prime factors, 31 is notable as a Mersenne prime (2^5 − 1). The combination 3×5×7×31 serves as an example of a small, square-free composite number used to illustrate properties of divisors and multiplicative arithmetic functions.