Practical numbers: Difference between revisions

=={{header|Julia}}==

{{trans|Python}}

<lang julia>using Primes

""" proper divisors of n """

function proper_divisors(n)

f = [one(n)]

for (p,e) in factor(n)

f = reduce(vcat, [f*p^j for j in 1:e], init=f)

end

pop!(f)

return f

end

""" return true if any subset of f sums to n. """

function sumofanysubset(n, f)

n in f && return true

total = sum(f)

n == total && return true

n > total && return false

rf = reverse(f)

d = n - popfirst!(rf)

return (d in rf) || (d > 0 && sumofanysubset(d, rf)) || sumofanysubset(n, rf)

end

function ispractical(n)

n == 1 && return true

isodd(n) && return false

f = proper_divisors(n)

return all(i -> sumofanysubset(i, f), 1:n-1)

end

const prac333 = filter(ispractical, 1:333)

println("There are ", length(prac333), " practical numbers between 1 to 333 inclusive.")

println("Start and end: ", filter(x -> x < 25, prac333), " ... ", filter(x -> x > 287, prac333), "\n")

for n in [666, 6666, 66666, 222222]

println("$n is ", ispractical(n) ? "" : "not ", "a practical number.")

end

</lang>{{out}}

<pre>

There are 77 practical numbers between 1 to 333 inclusive.

Start and end: [1, 2, 4, 6, 8, 12, 16, 18, 20, 24] ... [288, 294, 300, 304, 306, 308, 312, 320, 324, 330]

666 is a practical number.

6666 is a practical number.

66666 is not a practical number.

222222 is a practical number.

</pre>