A242460 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.

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, 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, 2, 0, 2, 0, 2, 3, 2, 2, 2, 0, 3, 2, 2, 0, 2, 2, 2, 2, 2

Offset

2,3

Comments

Primes and powers have a(n) = 0.

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 2..100000

Example

1750 can be factored in the following ways, resulting in product expressions: (number of factors)*(max factor - min factor)
   1750 = 2*5*5*5*7 => (5)*(7-2) = 25,
   1750 = 35*50     => (2)*(50-35) = 30,
   1750 = 5*5*7*10  => (4)*(10-5) = 20.
This last factoring gives the product 20 which is the lowest possible and therefore 1750 will split into 4 factors; so a(1750) = 4.

Crossrefs

Sequence in context: A153585 A169611 A374637 * A144494 A136166 A259525

Adjacent sequences: A242457 A242458 A242459 * A242461 A242462 A242463

Keyword

nonn,easy

Author

Gordon Hamilton, May 15 2014

Extensions

a(33)-a(94) from Hiroaki Yamanouchi, Mar 25 2015

Status

approved