Ruth-Aaron numbers: Difference between revisions
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First Ruth-Aaron triple (divisors): 89460294
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=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
{These routines would normally be in a library, but are shown here for clarity}
function IsPrime(N: int64): boolean;
{Fast, optimised prime test}
var I,Stop: int64;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N+0.0));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;
procedure StoreNumber(N: integer; var IA: TIntegerDynArray);
{Expand and store number in array}
begin
SetLength(IA,Length(IA)+1);
IA[High(IA)]:=N;
end;
procedure GetPrimeFactors(N: integer; var Facts: TIntegerDynArray);
{Get all the prime factors of a number}
var I: integer;
begin
I:=2;
SetLength(Facts,0);
repeat
begin
if (N mod I) = 0 then
begin
StoreNumber(I,Facts);
N:=N div I;
end
else I:=GetNextPrime(I);
end
until N=1;
end;
procedure GetPrimeDivisors(N: integer; var Facts: TIntegerDynArray);
{Get all unique prime factors of a number}
var I: integer;
begin
I:=2;
SetLength(Facts,0);
repeat
begin
if (N mod I) = 0 then
begin
StoreNumber(I,Facts);
N:=N div I;
while (N mod I) = 0 do N:=N div I;
end
else I:=GetNextPrime(I);
end
until N=1;
end;
{------------------------------------------------------------}
procedure RuthAaronNumbers(Memo: TMemo; UseFactors: boolean);
var N,Sum1,Sum2,Cnt: integer;
var S: string;
function GetFactorSum(N: integer): integer;
{Get the sum of the prime factors or divisors}
var IA: TIntegerDynArray;
var I: integer;
begin
if UseFactors then GetPrimeFactors(N,IA)
else GetPrimeDivisors(N,IA);
Result:=0;
for I:=0 to High(IA) do Result:=Result+IA[I];
end;
begin
Cnt:=0;
S:='';
{Get first sum}
Sum1:=GetFactorSum(1);
for N:=1 to High(integer) do
begin
{Get next sum}
Sum2:=GetFactorSum(N+1);
{Look for matching sums = Ruth-Aaron numbers}
if Sum1=Sum2 then
begin
Inc(Cnt);
S:=S+Format('%6D',[N]);
if Cnt>=30 then break;
If (Cnt mod 10)=0 then S:=S+CRLF;
end;
Sum1:=Sum2;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('Count = '+IntToStr(Cnt));
end;
procedure ShowRuthAaronNumbers(Memo: TMemo);
begin
Memo.Lines.Add('The first 30 Ruth-Aaron numbers using factors');
RuthAaronNumbers(Memo, True);
Memo.Lines.Add('The first 30 Ruth-Aaron numbers using divisors');
RuthAaronNumbers(Memo, False);
end;
</syntaxhighlight>
{{out}}
<pre>
The first 30 Ruth-Aaron numbers using factors
5 8 15 77 125 714 948 1330 1520 1862
2491 3248 4185 4191 5405 5560 5959 6867 8280 8463
10647 12351 14587 16932 17080 18490 20450 24895 26642 26649
Count = 30
The first 30 Ruth-Aaron numbers using divisors
5 24 49 77 104 153 369 492 714 1682
2107 2299 2600 2783 5405 6556 6811 8855 9800 12726
13775 18655 21183 24024 24432 24880 25839 26642 35456 40081
Count = 30
Elapsed Time: 5.991 Sec.
</pre>
=={{header|Factor}}==
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