ROSECODE 386

Fair partition

Philippe_57721 · Programming · 2017-03-24

The number

10! = 3628800

has a set

D

of 270 divisors.

We can find 2 sets

D_{1}

and

D_{2}

such as
- the product of each element of

D_{1}

with each element of

D_{2}

generates

D

- the cardinals of the sets

D_{1}

and

D_{2}

are the closest possible

D_{1} = {1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025}

and

| D_{1} | = 15

D_{2} = {1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 896, 1792}

and

| D_{2} | = 18

Find a fair partition for

100!

Answer format:

| D_{1} |, | D_{2} |

(in ascending order)

Example: 15,18

[My timing: 54 sec]