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Distinct terms in a multiplication table

Problem 466

Published on 06 April 2014 at 07:00 am [Server Time]

Let P(m,n) be the number of distinct terms in an m×n multiplication table.

For example, a 3×4 multiplication table looks like this:

× 1234
1 1234
2 2468
3 36912

There are 8 distinct terms {1,2,3,4,6,8,9,12}, therefore P(3,4) = 8.

You are given that:
P(64,64) = 1263,
P(12,345) = 1998, and
P(32,1015) = 13826382602124302.

Find P(64,1016).


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