Duffinian numbers: Difference between revisions
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(166463, 166464, 166465) (167041, 167042, 167043)
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=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
{These subroutines would normally be in a library, but is included here for clarity}
function GetAllProperDivisors(N: Integer;var IA: TIntegerDynArray): integer;
{Make a list of all the "proper dividers" for N}
{Proper dividers are the of numbers the divide evenly into N}
var I: integer;
begin
SetLength(IA,0);
for I:=1 to N-1 do
if (N mod I)=0 then
begin
SetLength(IA,Length(IA)+1);
IA[High(IA)]:=I;
end;
Result:=Length(IA);
end;
function GetAllDivisors(N: Integer;var IA: TIntegerDynArray): integer;
{Make a list of all the "proper dividers" for N, Plus N itself}
begin
Result:=GetAllProperDivisors(N,IA)+1;
SetLength(IA,Length(IA)+1);
IA[High(IA)]:=N;
end;
function IsDuffinianNumber(N: integer): boolean;
{Test number to see if it a Duffinian number}
var Facts1,Facts2: TIntegerDynArray;
var Sum,I,J: integer;
begin
Result:=False;
{Must be a composite number}
if IsPrime(N) then exit;
{Get all divisors}
GetAllDivisors(N,Facts1);
{Get sum of factors}
Sum:=0;
for I:=0 to High(Facts1) do
Sum:=Sum+Facts1[I];
{Get all factor of Sum}
GetAllDivisors(Sum,Facts2);
{Test if the two number share any factors}
for I:=1 to High(Facts1) do
for J:=1 to High(Facts2) do
if Facts1[I]=Facts2[J] then exit;
{If not, they are relatively prime}
Result:=True;
end;
procedure ShowDuffinianNumbers(Memo: TMemo);
var N,Cnt,D1,D2,D3: integer;
var S: string;
begin
Cnt:=0;
S:='';
Memo.Lines.Add('First 50 Duffinian Numbers');
for N:=2 to high(integer) do
if IsDuffinianNumber(N) then
begin
Inc(Cnt);
S:=S+Format('%5d',[N]);
if (Cnt mod 10)=0 then S:=S+CRLF;
if Cnt>=50 then break;
end;
Memo.Lines.Add(S);
D1:=0; D2:=-10; D3:=0;
S:=''; Cnt:=0;
Memo.Lines.Add('First 15 Duffinian Triples');
for N:=2 to high(integer) do
if IsDuffinianNumber(N) then
begin
D1:=D2; D2:=D3;
D3:=N;
if ((D2-D1)=1) and ((D3-D2)=1) then
begin
Inc(Cnt);
S:=S+Format('(%5d%5d%5d) ',[D1,D2,D3]);
if (Cnt mod 3)=0 then S:=S+CRLF;
if Cnt>=15 then break;
end;
end;
Memo.Lines.Add(S);
end;
</syntaxhighlight>
{{out}}
<pre>
First 50 Duffinian Numbers
4 8 9 16 21 25 27 32 35 36
39 49 50 55 57 63 64 65 75 77
81 85 93 98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217
First 20 Duffinian Triples
( 63 64 65) ( 323 324 325) ( 511 512 513)
( 721 722 723) ( 899 900 901) ( 1443 1444 1445)
( 2303 2304 2305) ( 2449 2450 2451) ( 3599 3600 3601)
( 3871 3872 3873) ( 5183 5184 5185) ( 5617 5618 5619)
( 6049 6050 6051) ( 6399 6400 6401) ( 8449 8450 8451)
( 10081 10082 10083) ( 10403 10404 10405) ( 11663 11664 11665)
( 12481 12482 12483) ( 13447 13448 13449)
Elapsed Time: 825.340 ms.
</pre>
=={{header|Factor}}==
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