n-digit numbers with n factors, each with a different number of digits

[Joerg Arndt]

* N. J. A. Sloane <njas at research.att.com> [Dec 13. 2006 09:56]:
> Joshua,  Just to get the ball rolling, I am adding this:
> 
> Comments and corrections welcomed!
> 
> Neil
> 
> 
> %I A125315
> %S A125315 1,11,121,1111,14641,112211,1771561,11117777,123187801,1464143923,
> %T A125315 25937424601
> %N A125315 Smallest n-digit number that has exactly n factors, each with a different num
> ber of digits.
> %O A125315 0,2
> %K A125315 nonn,base
> %A A125315 Joshua Zucker (joshua.zucker(AT)gmail.com), Dec 11 2006

I seem to not understand the definition:
11: 11
121: 11 11
1111: 11 101
14641: 11 11 11 11
112211: 11 101 101
1771561: 11 11 11 11 11 11
11117777: 11 101 10007
123187801: 11 11 1009 1009
1464143923: 11 11 11 11 100003
25937424601: 11 11 11 11 11 11 11 11 11 11

That part:
> each with a different number of digits.
apparently doesn't concern the factors.
But when it means the numbers themselves, it is superfluous.