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n-digit numbers having n divisors each with a different number of digits.
2

%I #7 May 13 2013 01:54:09

%S 1,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,121,

%T 169,289,361,529,841,961,1111,1133,1177,1199,1243,1313,1331,1339,1391,

%U 1397,1417,1441,1469,1507,1529,1639,1651,1661,1703,1717,1727,1751,1781

%N n-digit numbers having n divisors each with a different number of digits.

%C A subsequence of A095862.

%H Charles R Greathouse IV, <a href="/A125845/b125845.txt">Table of n, a(n) for n = 1..10000</a>

%H Sam Vandervelde, <a href="http://www.mandelbrot.org">The Mandelbrot Competition</a>, round 2, 2006-07, asked for the smallest composite number in this list.

%e 1 is the only one-digit number with only one factor. Two-digit primes are the only two-digit numbers in the list since they have a one-digit factor (1) and a two-digit factor (themselves). Three-digit squares of two-digit primes are the only three-digit numbers in the list, since only numbers of the form p^2 can have three factors.

%Y A125315 gives the smallest n-digit number of this form for each n.

%K base,nonn

%O 1,2

%A _Joshua Zucker_, Dec 11 2006