Data commit

Task/Mertens-function/Nim/mertens-function.nim

@@ -0,0 +1,34 @@
+import sequtils, strformat
+
+func mertensNumbers(max: int): seq[int] =
+  result = repeat(1, max + 1)
+  for n in 2..max:
+    for k in 2..n:
+      dec result[n], result[n div k]
+
+const Max = 1000
+let mertens = mertensNumbers(Max)
+
+echo "First 199 Mertens numbers:"
+const Count = 200
+var column = 0
+for i in 0..<Count:
+  if column > 0: stdout.write ' '
+  stdout.write if i == 0: "  " else: &"{mertens[i]:>2}"
+  inc column
+  if column == 20:
+    stdout.write '\n'
+    column = 0
+
+var zero, cross, previous = 0
+for i in 1..Max:
+  let m = mertens[i]
+  if m == 0:
+    inc zero
+    if previous != 0:
+      inc cross
+  previous = m
+
+echo ""
+echo &"M(n) is zero {zero} times for 1 ⩽ n ⩽ {Max}."
+echo &"M(n) crosses zero {cross} times for 1 ⩽ n ⩽ {Max}."