= Trial-division divisor counting
Factor a <positive integer> while multiplying the exponent-plus-one contributions to its <divisor> count. After removing all prime factors below the current trial factor, a trial factor that divides the remainder must itself be prime. Remove its full power and advance. Once the trial factor's square exceeds the remainder, any remainder greater than one is prime and contributes a factor two. The <invariant> separates the original <integer> into removed <prime powers> and the remaining coprime factor; no factor <array> is necessary.
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