Data commit

Task/Untouchable-numbers/Julia/untouchable-numbers.julia

@@ -0,0 +1,33 @@
+using Primes
+
+function properfactorsum(n)
+    f = [one(n)]
+    for (p,e) in factor(n)
+        f = reduce(vcat, [f*p^j for j in 1:e], init=f)
+    end
+    pop!(f)
+    return sum(f)
+end
+
+const maxtarget, sievelimit = 1_000_000, 512_000_000
+const untouchables = ones(Bool, maxtarget)
+
+for i in 2:sievelimit
+    n = properfactorsum(i)
+    if n <= maxtarget
+        untouchables[n] = false
+    end
+end
+for i in 6:maxtarget
+    if untouchables[i] && (isprime(i - 1) || isprime(i - 3))
+        untouchables[i] = false
+    end
+end
+
+println("The untouchable numbers ≤ 2000 are: ")
+for (i, n) in enumerate(filter(x -> untouchables[x], 1:2000))
+    print(rpad(n, 5), i % 10 == 0 || i == 196 ? "\n" : "")
+end
+for N in [2000, 10, 100, 1000, 10_000, 100_000, 1_000_000]
+    println("The count of untouchable numbers ≤ $N is: ", count(x -> untouchables[x], 1:N))
+end