func mertens(n) is cached {

    var lookup_size    = (2 * n.iroot(3)**2)
    var mertens_lookup = [0]

    for k in (1..lookup_size) {
        mertens_lookup[k] = (mertens_lookup[k-1] + k.moebius)
    }

    static cache = Hash()

    func (n) {

        if (n <= lookup_size) {
            return mertens_lookup[n]
        }

        if (cache.has(n)) {
            return cache{n}
        }

        var M = 1
        var s = n.isqrt

        for k in (2 .. floor(n/(s+1))) {
            M -= __FUNC__(floor(n/k))
        }

        for k in (1..s) {
            M -= (mertens_lookup[k] * (floor(n/k) - floor(n/(k+1))))
        }

        cache{n} = M
    }(n)
}