p021.jl

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Amicable numbers

Problem 21

Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.
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include("utils/divisors.jl")

function d(n)
 if n == 1
  return(0)
 else
  return sum(proper_divisors(n))
 end
end

N = 10000
total = 0

for n=2:N-1
 dn = d(n)
 ddnn = d(dn)
 if (n == ddnn) & (n != dn)
  print("amicable! $n and $dn \n")
  global total += n
 end
end

print("sum of amicable numbers <$N is: $total \n")