Data commit

Task/M-bius-function/AutoHotkey/m-bius-function.ahk

@@ -0,0 +1,46 @@
+loop 100
+    result .= SubStr("  " Möbius(A_Index), -1) . (Mod(A_Index, 10) ? "  " : "`n")
+MsgBox, 262144, , % result
+return
+
+Möbius(n){
+    if n=1
+        return 1
+    x := prime_factors(n)
+    c := x.Count()
+    sq := []
+    for i, v in x
+        if sq[v]
+            return 0
+        else
+            sq[v] := 1
+    return (c/2 = floor(c/2)) ? 1 : -1
+}
+
+prime_factors(n) {
+    if (n <= 3)
+        return [n]
+    ans := [], done := false
+    while !done {
+        if !Mod(n, 2)
+            ans.push(2), n /= 2
+        else if !Mod(n, 3)
+            ans.push(3), n /= 3
+        else if (n = 1)
+            return ans
+        else {
+            sr := sqrt(n), done := true, i := 6
+            while (i <= sr+6) {
+                if !Mod(n, i-1) { ; is n divisible by i-1?
+                    ans.push(i-1), n /= i-1, done := false
+                    break
+                }
+                if !Mod(n, i+1) { ; is n divisible by i+1?
+                    ans.push(i+1), n /= i+1, done := false
+                    break
+                }
+                i += 6
+    }}}
+    ans.push(Format("{:d}", n))
+    return ans
+}