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number of distinct prime divisors of n

Source: Brazilian TST 1999

May 2, 2005
number theory unsolvednumber theory

Problem Statement

For a positive integer n, let w(n)w(n) denote the number of distinct prime divisors of n. Determine the least positive integer k such that 2w(n)≤kn42^{w(n)} \leq k \sqrt[4]{n} for all positive integers n.
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