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An important function in number theory is ... , the number of integers in the range ... that have an even number of prime factors minus the number of integers in that range that have an odd number of prime factors. This function is nicely expressible as a sum of values of Liouville's function: ... , where ... is the number or prime factors of ... , via ... . The graph of ... is an irregular step function. This Demonstration illustrates the remarkable fact that we can approximate the jumps of this step function by using a sum that involves zeros of the Riemann zeta function ... .
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