# Problem 159: Digital root sums of factorisations
A composite number can be factored many different ways. For instance,
not including multiplication by one, 24 can be factored in 7 distinct
ways: 24 = 2x2x2x3 24 = 2x3x4 24 = 2x2x6 24 = 4x6 24 = 3x8 24 = 2x12 24
= 24 Recall that the digital root of a number, in base 10, is found by
adding together the digits of that number, and repeating that process
until a number is arrived at that is less than 10. Thus the digital root
of 467 is 8. We shall call a Digital Root Sum (DRS) the sum of the
digital roots of the individual factors of our number. The chart below
demonstrates all of the DRS values for 24. FactorisationDigital Root
Sum2x2x2x3 92x3x4 92x2x6 104x6 103x8 112x12 524 6The maximum Digital
Root Sum of 24 is 11. The function mdrs(n) gives the maximum Digital
Root Sum of n. So mdrs(24)=11. Find ∑mdrs(n) for 1 < n <
1,000,000.