Data commit

Task/Mertens-function/Julia/mertens-function.julia

@@ -0,0 +1,57 @@
+using Primes, Formatting
+
+function moebius(n::Integer)
+    @assert n > 0
+    m(p, e) = p == 0 ? 0 : e == 1 ? -1 : 0
+    return reduce(*, m(p, e) for (p, e) in factor(n) if p  ≥ 0; init=1)
+end
+μ(n) = moebius(n)
+
+mertens(x) = sum(n -> μ(n), 1:x)
+M(x) = mertens(x)
+
+print("First 99 terms of the Mertens function for positive integers:\n   ")
+for n in 1:99
+    print(lpad(M(n), 3), n % 10 == 9 ? "\n" : "")
+end
+
+function maximinM(N)
+    z, cros, lastM, maxi, maxM, mini, minM, sumM, pos, neg = 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
+    for i in 1:N
+        m = μ(i) + lastM
+        if m == 0 && lastM != 0
+            cros += 1
+        end
+        sumM += m
+        lastM = m
+        if m > maxM
+            maxi = i
+            maxM = m
+        elseif m < minM
+            mini = i
+            minM = m
+        end
+        if m > 0
+            pos += 1
+        elseif m < 0
+            neg += 1
+        else
+            z += 1
+        end
+    end
+    println("\nFor M(x) with x from 1 to $(format(N, commas=true)):")
+    println("The maximum of M(x) is M($(format(maxi, commas=true)) = $maxM.")
+    println("The minimum of M(x) is M($(format(mini, commas=true))) = $minM.")
+    println("The sum of M(x) is $(format(sumM, commas=true)).")
+    println("The count of positive M(x) is $(format(pos, commas=true)), count of negative M(x) is $(format(neg, commas=true)).")
+    println("M(x) has $(format(z, commas=true)) zeroes in the interval.")
+    println("M(x) has $(format(cros, commas=true)) crossings in the interval.")
+    diff = pos - neg
+    if diff > 0
+        println("Positive M(x) exceed negative ones by $(format(diff, commas=true)).")
+    else
+        println("Negative M(x) exceed positive ones by $(format(-diff, commas=true)).")
+    end
+end
+
+foreach(maximinM, (1000, 1_000_000, 1_000_000_000))