A242460 - OEIS

%I #15 Dec 27 2020 19:26:25

%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)*(7-2) = 25,

%e    1750 = 35*50     => (2)*(50-35) = 30,

%e    1750 = 5*5*7*10  => (4)*(10-5) = 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