Family Day update

Task/Arithmetic-Rational/Julia/arithmetic-rational.julia

@@ -1,24 +1,7 @@
-function isperfect{T<:Integer}(n::T)
-    !isprime(n) || return false
-    tal = 1//n
-    hi = isqrt(n)
-    if hi^2 == n
-        tal += 1//hi
-        hi -= 1
-    end
-    for i in 2:hi
-        (d, r) = divrem(n, i)
-        if r == 0
-            tal += (1//i + 1//d)
-        end
-    end
-    return tal == 1//1
-end
+using Primes
+divisors(n) = foldl((a, (p, e)) -> vcat((a * [p^i for i in 0:e]')...), factor(n), init=[1])
 
-lo = 2
-hi = 2^19
-println("Searching for perfect numbers from ", lo, " to ", hi, ".")
-for i in 2:2^19
-    isperfect(i) || continue
-    println(@sprintf("%8d", i))
-end
+isperfect(n) = sum(1 // d for d in divisors(n)) == 2
+
+lo, hi = 2, 2^19
+println("Perfect numbers between ", lo, " and ", hi, ": ", collect(filter(isperfect, lo:hi)))