Multiply-Then-Add "Game"
- From: "Leroy Quet" <qqquet@xxxxxxxxxxxxxx>
- Date: 4 Jan 2007 11:02:53 -0800
I wonder what the sequence is of maximal scores (for n integers)
of the game defined below.
-
First, for a given n, each player partitions the sequence of
the first n positive integers into the two sets {a(k)} and {b(k)}.
A player's score is the number of positive divisors of the sum:
product a(k)'s + product b(k)'s.
So, for example, if n = 6, a player may have the sum of the products:
1*3*4*5 + 2*6 = 72.
Since 72 has 12 positive divisors, the player gets 12 points.
-
Allowing for empty sets (so a(1) can be defined), I get that
the maximum scores sequence begins:
2, 2, 2, 4,...
Thanks,
Leroy Quet
.
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