## Distinct terms in a multiplication table

### Problem 466

Published on Sunday, 6th April 2014, 07:00 am; Solved by 148Let 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:

× | 1 | 2 | 3 | 4 |
---|---|---|---|---|

1 | 1 | 2 | 3 | 4 |

2 | 2 | 4 | 6 | 8 |

3 | 3 | 6 | 9 | 12 |

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(32,10^{15}) = 13826382602124302.

Find P(64,10^{16}).