prevprod

prevprod([k_1,k_2,...], n)

Previous integer not greater than `n` that can be written as \$\prod k_i^{p_i}\$ for integers \$p_1\$, \$p_2\$, etc.

Examples

In the Julia programming language, the function `prevprod([k_1, k_2, ...], n)` returns the previous integer not greater than `n` that can be written as the product of the integers `k_1^p_1`, `k_2^p_2`, etc., where `p_1`, `p_2`, etc. are integers.

1. Find the previous product less than or equal to a given number:

``````julia> prevprod([2, 3, 5], 100)
96``````

This example finds the previous integer not greater than 100 that can be written as the product of 2^p, 3^q, and 5^r.

2. Calculate the previous product for a larger set of integers:

``````julia> prevprod([2, 3, 5, 7, 11], 1000)
990``````

It returns the previous integer not greater than 1000 that can be expressed as the product of 2^p, 3^q, 5^r, 7^s, and 11^t.

3. Handle the case when the given number itself is a product:
``````julia> prevprod([2, 3, 5], 30)
30``````

In this example, the given number 30 can be expressed as the product of 2^1, 3^1, and 5^1 itself. So, it returns the same number.

Common mistake example:

``````julia> prevprod([2, 3, 5], 10)
ERROR: ArgumentError: The number 10 cannot be expressed as the product of the given factors.``````

In this case, the function raises an error because there is no integer less than or equal to 10 that can be expressed as the product of 2^p, 3^q, and 5^r. It's important to ensure that the given number can be represented as a valid product before using the `prevprod` function.

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