MODULE PerfectTotient;
FROM InOut IMPORT WriteCard, WriteLn;

CONST Amount = 20;
VAR n, seen: CARDINAL;

PROCEDURE GCD(a, b: CARDINAL): CARDINAL;
VAR c: CARDINAL;
BEGIN
    WHILE b # 0 DO
        c := a MOD b;
        a := b;
        b := c;
    END;
    RETURN a;
END GCD;

PROCEDURE Totient(n: CARDINAL): CARDINAL;
VAR i, tot: CARDINAL;
BEGIN
    tot := 0;
    FOR i := 1 TO n/2 DO
        IF GCD(n,i) = 1 THEN
            tot := tot + 1;
        END;
    END;
    RETURN tot;
END Totient;

PROCEDURE Perfect(n: CARDINAL): BOOLEAN;
VAR sum, x: CARDINAL;
BEGIN
    sum := 0;
    x := n;
    REPEAT
        x := Totient(x);
        sum := sum + x;
    UNTIL x = 1;
    RETURN sum = n;
END Perfect;

BEGIN
    seen := 0;
    n := 3;
    WHILE seen < Amount DO
        IF Perfect(n) THEN
            WriteCard(n,5);
            seen := seen + 1;
            IF seen MOD 14 = 0 THEN
                WriteLn();
            END;
        END;
        n := n + 2;
    END;
    WriteLn();
END PerfectTotient.