Data update

Task/Arithmetic-derivative/Mathematica/arithmetic-derivative.math

@@ -0,0 +1,32 @@
+(* Arithmetic derivative *)
+
+ClearAll[d, twoFactorsOf];
+
+twoFactorsOf[n_Integer?Positive] := Module[{factors = FactorInteger[n, 2], p, factor},
+   If[Length[factors] == 1,
+       factor = Flatten@factors;
+        p = First@factor;
+        factors = {factor - {0, 1}, {p, 1}};
+   ];
+   Return[Power@@@factors];
+];
+
+twoFactorsOf[n_Integer?Negative] := twoFactorsOf[-n] * {-1, -1};
+
+d[0] = d[1] = 0;
+d[p_Integer?PrimeQ] := 1;
+d[n_Integer?Negative] := -d[-n];
+d[mn_Integer] := Module[{m, n},
+   {m, n} = twoFactorsOf[m n];
+   Return[d[m] n + m d[n]];
+];
+
+SetAttributes[d, Listable];
+
+(* Output *)
+
+Partition[StringPadLeft[ToString /@ d[Range[-99, 100]], 5], UpTo[10]] // TableForm
+
+StringJoin["d[10^", ToString@First[#], "]", If[First[#] <= 9, "  ", " "], "/ 7",
+    " = ",
+    ToString@Last[#]] & /@ Table[{n, d[10^n]/7}, {n, 1, 20}] // TableForm