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util/julia/files/_erastothenes_extended_sieve.jl

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+include("_erastothenes_sieve.jl")
+include("_math.jl")
+
+mutable struct extended_sieve
+    sieve::sieve
+    factors::Vector{Vector{Int}}
+end
+
+function get_extended_sieve()
+    return extended_sieve(sieve(falses(1), 1, 1, 1000), [[]])
+end
+
+function _elongate!(es::extended_sieve)
+    s = es.sieve
+    length = s._length
+    target = s._target
+    diff = target - length
+    run!(s, target)
+
+    factors = append!(es.factors, fill([], nneg(diff)))
+    done = [trues(length); falses(diff)]
+    if diff > 0
+        for i ∈ get_primes(s)
+            if i > length
+                factors[i] = [i]
+            end
+            for j ∈ cld(length+1, i):fld(target, i)
+                prod = i*j
+                if ~done[prod]
+                    if done[j]
+                        index = searchsortedfirst(factors[j], i)
+                        factors[prod] = insert!(copy(factors[j]), index, i)
+                        done[prod] = true
+                    else
+                        push!(factors[prod], i)
+                    end
+                end
+            end
+        end
+    end
+    return Nothing
+end
+
+function run!(es::extended_sieve, n::Int)
+    es.sieve._target = n;
+    _elongate!(es)
+    return Nothing
+end
+
+function get(es::extended_sieve, n::Int, prerun=true::Bool)
+    if n > es.sieve._length
+        run(s, prerun ? n + es.sieve._prerun_size : n)
+    end
+    return (es.sieve[n], es.factors[n])
+end
+
+function get_primes(es::extended_sieve)
+    return get_primes(es.sieve)
+end