%I
%S 0,0,2,0,2,0,3,2,2,0,2,0,2,2,2,0,3,0,2,2,2,0,2,2,2,3,2,0,2,0,5,2,2,2,
%T 2,0,2,2,2,0,2,0,2,3,2,0,3,2,3,2,2,0,4,2,2,2,2,0,3,0,2,2,2,2,2,0,2,2,
%U 2,0,2,0,2,3,2,2,2,0,3,2,2,0,2,2,2,2,2
%N Integers in the Hadron Collider: Composite integers, n, break apart into a(n)>=2 factors in order to minimize the product: (number of factors)*(max factor  min factor). In case of ties, a(n) is chosen to be as small as possible.
%C Primes and powers have a(n) = 0.
%H Hiroaki Yamanouchi, <a href="/A242460/b242460.txt">Table of n, a(n) for n = 2..100000</a>
%e 1750 can be factored in the following ways, resulting in product expressions: (number of factors)*(max factor  min factor)
%e 1750 = 2*5*5*5*7 => (5)*(72) = 25,
%e 1750 = 35*50 => (2)*(5035) = 30,
%e 1750 = 5*5*7*10 => (4)*(105) = 20.
%e This last factoring gives the product 20 which is the lowest possible and therefore 1750 will split into 4 factors; so a(1750) = 4.
%K nonn,easy
%O 2,3
%A _Gordon Hamilton_, May 15 2014
%E a(33)a(94) from _Hiroaki Yamanouchi_, Mar 25 2015
