Abundant odd numbers: Difference between revisions

</pre>

=={{header|ALGOL W}}==

{{Trans|ALGOL 68}}

Using the divisor_sum procedure from the [[Sum_of_divisors#ALGOL_W]] task.

<lang algolw>begin

% find some abundant odd numbers - numbers where the sum of the proper %

% divisors is bigger than the number %

% itself %

% computes the sum of the divisors of v using the prime %

% factorisation %

integer procedure divisor_sum( integer value v ) ; begin

integer total, power, n, p;

total := 1; power := 2; n := v;

% Deal with powers of 2 first %

while not odd( n ) do begin

total := total + power;

power := power * 2;

n := n div 2

end while_not_odd_n ;

% Odd prime factors up to the square root %

p := 3;

while ( p * p ) <= n do begin

integer sum;

sum := 1;

power := p;

while n rem p = 0 do begin

sum := sum + power;

power := power * p;

n := n div p

end while_n_rem_p_eq_0 ;

p := p + 2;

total := total * sum

end while_p_x_p_le_n ;

% If n > 1 then it's prime %

if n > 1 then total := total * ( n + 1 );

total

end divisor_sum ;

% returns the sum of the proper divisors of v %

integer procedure divisorSum( integer value v ) ;

if v < 2 then 1 else divisor_sum( v ) - v;

% find numbers required by the task %

begin

integer aCount, oddNumber, dSum;

logical foundOddAn;

% first 25 odd abundant numbers %

oddNumber := 1;

aCount := 0;

write( "The first 25 abundant odd numbers:" );

while aCount < 25 do begin

dSum := divisorSum( oddNumber );

if dSum > oddNumber then begin

aCount := aCount + 1;

write( i_w := 6, oddNumber, " proper divisor sum: ", dSum )

end if_dSum_gt_oddNumber ;

oddNumber := oddNumber + 2

end while_aCount_lt_1000 ;

% 1000th odd abundant number %

while aCount < 1000 do begin

dSum := divisorSum( oddNumber );

if dSum > oddNumber then aCount := aCount + 1;

oddNumber := oddNumber + 2

end while_aCount_lt_1000 ;

write( "1000th abundant odd number: " );

write( oddNumber - 2, " proper divisor sum: ", dSum );

% first odd abundant number > one billion %

oddNumber := 1000000001;

foundOddAn := false;

while not foundOddAn do begin

dSum := divisorSum( oddNumber );

if dSum > oddNumber then begin

foundOddAn := true;

write( "First abundant odd number > 1000000000: " );

write( oddNumber, " proper divisor sum: ", dSum )

end if_dSum_gt_oddNumber ;

oddNumber := oddNumber + 2

end while_not_foundOddAn ;

end

end.</lang>

{{out}}

<pre>

The first 25 abundant odd numbers:

945 proper divisor sum: 975

1575 proper divisor sum: 1649

2205 proper divisor sum: 2241

2835 proper divisor sum: 2973

3465 proper divisor sum: 4023

4095 proper divisor sum: 4641

4725 proper divisor sum: 5195

5355 proper divisor sum: 5877

5775 proper divisor sum: 6129

5985 proper divisor sum: 6495

6435 proper divisor sum: 6669

6615 proper divisor sum: 7065

6825 proper divisor sum: 7063

7245 proper divisor sum: 7731

7425 proper divisor sum: 7455

7875 proper divisor sum: 8349

8085 proper divisor sum: 8331

8415 proper divisor sum: 8433

8505 proper divisor sum: 8967

8925 proper divisor sum: 8931

9135 proper divisor sum: 9585

9555 proper divisor sum: 9597

9765 proper divisor sum: 10203

10395 proper divisor sum: 12645

11025 proper divisor sum: 11946

1000th abundant odd number:

492975 proper divisor sum: 519361

First abundant odd number > 1000000000:

1000000575 proper divisor sum: 1083561009