540radical
540radical refers to the radical of the integer 540 in number theory, denoted rad(540). The radical of a positive integer n is defined as the product of its distinct prime factors. If n = p1^a1 p2^a2 ... pk^ak, then rad(n) = p1 p2 ... pk. For 540, the prime factorization is 540 = 2^2 × 3^3 × 5, so the distinct primes are 2, 3 and 5, and rad(540) = 2 × 3 × 5 = 30.
Properties of the radical function include that rad(n) is always squarefree (no repeated prime factors) and
Context and applications: the radical function rad(n) appears in various areas of number theory, particularly in
Examples: rad(240) = 2 × 3 × 5 = 30, since 240 = 2^4 × 3 × 5. rad(1) is