Some sequences suggest themselves: Magic products of 3x3 multiplicative magic squares 216,1000,1728,2744,3375,4096,5832,8000,9261,10648,... These have to be cubes, so the sequence of roots would be nice 6,10,12,14,15,16,18,20,21,22,... These two are short but probably admissible: Least magic product of nxn multiplicative magic square (n >= 3) 216,5040,302400 Least magic product of nxn multiplicative semimagic square (n >= 3) 120,4320,277200 ----- Original Message ----- From: "Christian Boyer" <cboyer@club-internet.fr> To: "'math-fun'" <math-fun@mailman.xmission.com> Sent: Tuesday, October 04, 2005 5:48 AM Subject: [math-fun] Multiplicative squares

Website updated this morning!

Go to <http://www.multimagie.com/indexengl.htm> www.multimagie.com/indexengl.htm:

in the News of October 2005, there is a new page on multiplicative squares, including the results sent past week.

The 10 first magic products should be sufficient for the site, but I send to Neil the 30 first terms of each order (3x3, 4x4, and 5x5) for his EIS.

You will see that I've finally found a paper -published in 1983- already proving that the minimum product for 3x3 and 4x4 squares are 216 and 5040.

But, Rich, your nice and short proof on 216 is in my new page!

Christian.

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