Data commit

Task/Achilles-numbers/Delphi/achilles-numbers.delphi

@@ -0,0 +1,100 @@
+function GetTotient(N: integer): integer;
+{Calculate Euler's Totient}
+var M: integer;
+begin
+Result:= 0;
+for M:= 1 to N do
+ if GreatestCommonDivisor(M, N) = 1 then
+    Result:= Result+1;
+end;
+
+
+function IsPowerfulNum(N: integer): boolean;
+{Is a powerful number i.e. all prime factors square are divisor}
+var I: integer;
+var IA: TIntegerDynArray;
+begin
+Result:=False;
+GetPrimeFactors(N,IA);
+for I:=0 to High(IA) do
+ if (N mod (IA[I]*IA[I]))<>0 then exit;
+Result:=True;
+end;
+
+
+function CanBeMtoK(N: integer): boolean;
+{Can N be represented as M^K?}
+var M, A: integer;
+begin
+Result:=False;
+M:= 2;
+A:= M*M;
+repeat
+	begin
+	while true do
+		begin
+		if A = N then exit;
+                if A > N then break;
+                A:= A*M;
+                end;
+        M:= M+1;
+        A:= M*M;
+        end
+until   A > N;
+Result:=True;
+end;
+
+
+function IsAchilles(N: integer): boolean;
+{Achilles = Is Powerful and can be M^K}
+begin
+Result:=IsPowerfulNum(N) and CanBeMtoK(N);
+end;
+
+
+
+procedure AchillesNumbers(Memo: TMemo);
+var I,Cnt,Digits: integer;
+var S: string;
+var DigCnt: array [0..5] of integer;
+begin
+Memo.Lines.Add('First 50 Achilles numbers:');
+Cnt:=0; S:='';
+for I:=2 to high(Integer) do
+ if IsAchilles(I) then
+	begin
+	Inc(Cnt);
+	S:=S+Format('%6d',[I]);
+	if (Cnt mod 10)=0 then S:=S+CRLF;
+	if Cnt>=50 then break;
+	end;
+Memo.Lines.Add(S);
+
+Memo.Lines.Add('First 20 Strong Achilles Numbers:');
+Cnt:=0; S:='';
+for I:=2 to high(Integer) do
+ if IsAchilles(I) then
+   if IsAchilles(GetTotient(I)) then
+	begin
+	Inc(Cnt);
+	S:=S+Format('%6d',[I]);
+	if (Cnt mod 10)=0 then S:=S+CRLF;
+	if Cnt>=20 then break;
+	end;
+Memo.Lines.Add(S);
+
+Memo.Lines.Add('Digits Counts:');
+for I:=0 to High(DigCnt) do DigCnt[I]:=0;
+for I:=2 to high(Integer) do
+	begin
+	Digits:=NumberOfDigits(I);
+	if Digits>High(DigCnt) then break;
+	if IsAchilles(I) then Inc(DigCnt[Digits]);
+	end;
+Memo.Lines.Add('Last Count: '+IntToStr(I));
+for I:=0 to High(DigCnt) do
+ if DigCnt[I]>0 then
+	begin
+	Memo.Lines.Add(Format('%d digits: %d',[I,DigCnt[I]]));
+	end
+end;