Proper divisors: Difference between revisions

</pre>

=={{header|S-Basic}}==

<lang Basic>

$lines

$constant false = 0

$constant true = FFFFH

rem - compute p mod q

function mod(p, q = integer) = integer

end = p - q * (p/q)

rem - count, and optionally display, proper divisors of n

function divisors(n, display = integer) = integer

var i, limit, count, start, delta = integer

if mod(n, 2) = 0 then

begin

start = 2

delta = 1

end

else

begin

start = 3

delta = 2

end

count = 1

if display then print using "#####"; 1;

i = start

limit = n / start

while i <= limit do

begin

if mod(n, i) = 0 then

begin

if display then print using "#####"; i;

count = count + 1

end

i = i + delta

if count = 1 then limit = n / i

end

if display then print

end = count

rem - main program begins here

var i, ndiv, highdiv, highnum = integer

print "Proper divisors of first 10 numbers:"

for i = 1 to 10

print using "### : "; i;

ndiv = divisors(i, true)

next i

print "Searching for number with most divisors ..."

highdiv = 1

highnum = 1

for i = 1 to 20000

ndiv = divisors(i, false)

if ndiv > highdiv then

begin

highdiv = ndiv

highnum = i

end

next i

print "Searched up to"; i

print highnum; " has the most divisors: "; highdiv

end

</lang>

{{out}}

<pre>

Proper divisors of first 10 numbers:

1 : 1

2 : 1

3 : 1

4 : 1 2

5 : 1

6 : 1 2 3

7 : 1

8 : 1 2 4

9 : 1 3

10 : 1 2 5

Searching for number with most divisors ...

Searched up to 20000

15120 has the most divisors: 79