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.

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.
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.
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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prevprod

Examples

See Also

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