

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.


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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
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OFFSET

2,3


COMMENTS

Primes and powers have a(n) = 0.


LINKS



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)*(72) = 25,
1750 = 35*50 => (2)*(5035) = 30,
1750 = 5*5*7*10 => (4)*(105) = 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



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



