riddle

[Don Shepherd]

(12-11-2018 06:00 PM)Albert Chan Wrote:  223092870 = 2·3·5·7·11·13·17·19·23

This SS# had huge number of factors = 2^9 = 512

For valid SS# (i.e. 9 digits limits), what number have most factors ?

Edit: these 9-digits numbers have maximum of 1344 factors
http://math.univ-lyon1.fr/~nicolas/ramanujanNR.pdf, page 152

735134400 = 2^6 * 3^3 * 5^2 * 7 * 11 * 13 * 17
821620800 = 2^6 * 3^3 * 5^2 * 7 * 11 * 13 * 19
931170240 = 2^6 * 3^2 * 5 * 7 * 11 * 13 * 17 * 19
994593600 = 2^6 * 3^3 * 5^2 * 7 * 11 * 13 * 23

Albert, thanks for that reference. Very interesting.

I have a program on my 12c+ that can verify the number of factors pretty quickly.