How can I check if a lua table contains only sequential numeric indices?

How can I write a function that determines whether it's table argument is a true array?

isArray({1, 2, 4, 8, 16}) -> true
isArray({1, "two", 3, 4, 5}) -> true
isArray({1, [3]="two", [2]=3, 4, 5}) -> true
isArray({1, dictionaryKey = "not an array", 3, 4, 5}) -> false

I can't see any way of finding out if the numeric keys are the only keys.

ipairs iterates over indices 1..n, where n+1 is the first integer index with a nil value
pairs iterates over all keys.
if there are more keys than there are sequential indices, then it cannot be an array.

So all you have to do is see if the number of elements in pairs(table) is equal to the number of elements in ipairs(table)
the code can be written as follows:

function isArray(tbl)
    local numKeys = 0
    for _, _ in pairs(tbl) do
        numKeys = numKeys+1
    end
    local numIndices = 0
    for _, _ in ipairs(tbl) do
        numIndices = numIndices+1
    end
    return numKeys == numIndices
end

I'm pretty new to Lua, so there might be some builtin function to reduce the numKeys and numIndices calculations to simple function calls.