Practical numbers: Difference between revisions
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720 is a practical number.
222222 is a practical number.
</pre>
=={{header|Sidef}}==
Built-in:
<lang ruby>say is_practical(2**128 + 1) #=> false
say is_practical(2**128 + 4) #=> true</lang>
Slow implementation (as the task requires):
<lang ruby>func is_practical(n) {
var set = Set()
n.divisors.grep { _ < n }.subsets {|*a|
set << a.sum
}
1..n-1 -> all { set.has(_) }
}
var from = 1
var upto = 333
var list = (from..upto).grep { is_practical(_) }
say "There are #{list.len} practical numbers in the range #{from}..#{upto}."
say "#{list.first(10).join(', ')} ... #{list.last(10).join(', ')}\n"
for n in ([666, 6666, 66666]) {
say "#{'%5s' % n } is practical? #{is_practical(n)}"
}</lang>
Efficient algorithm:
<lang ruby>func is_practical(n) {
n.is_odd && return (n == 1)
n.is_pos || return false
var p = 1
var f = n.factor_exp
f.each_cons(2, {|a,b|
p *= sigma(a.head**a.tail)
b.head > (1 + p) && return false
})
return true
}</lang>
{{out}}
<pre>
There are 77 practical numbers in the range 1..333.
1, 2, 4, 6, 8, 12, 16, 18, 20, 24 ... 288, 294, 300, 304, 306, 308, 312, 320, 324, 330
666 is practical? true
6666 is practical? true
66666 is practical? false
</pre>
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