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

[David Wilson]

----- Original Message ----- 
From: "Joshua Zucker" <joshua.zucker at gmail.com>
To: "Sequence Fans" <seqfan at ext.jussieu.fr>
Sent: Tuesday, December 05, 2006 2:42 PM
Subject: n-digit numbers with n factors, each with a different number of 
digits


> But then I thought it might be even more fun to find the smallest
> n-digit number that has exactly n factors, each with a different
> number of digits.
>
> 1, 11, 121, 1111, 14641, 112211, 1771561, 11117777, 123187801,
> 1464143923, 25937424601, ...

The entire sequence is

1 11 121 1111 14641 112211 1771561 11117777 123187801 1144664411
25937424601 111255594439 3138428376721 11676721656611 125415159629881
1111777777824439 45949729863572161 112211673267009899 5559917313492231481
11141140678645587511 127682791131148878361 1215084337952324961011
81402749386839761113321 111177785564888344771073 1464275699906298123985921
12395075331451666927273211 123187802724629220036202249
1115674373475462386985328039

There is no 29-digit number with exactly 29 divisors, so the sequence ends 
here unless you want one of those evil "or 0 if no such number" sequences.