A132077 - OEIS

%I #11 Feb 23 2017 22:56:33

%S 1,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,

%T 113,131,151,169,181,191,199,211,223,227,229,233,277,289,311,313,331,

%U 337,353,361,373,383,433,443,449,499,529,557,577,599,661,677,727,733,757

%N Numbers having in decimal representation exactly the same number of distinct digits as number of divisors.

%C A043537(a(n)) = A000005(a(n)).

%C I believe a(n) ~ kn log n where k = 1/P(4) = 1/A085964, coming from numbers of the form p^4*q containing all ten decimal digits. - _Charles R Greathouse IV_, Feb 23 2017

%H R. Zumkeller, <a href="/A132077/b132077.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2) = 13: #{1,3} = #{1,13};

%e a(26) = 169: #{1,6,9} = #{1,13,169};

%e a(74) = 1027: #{0,1,2,7} = #{1,13,79,1027};

%e a(241) = 2197: #{1,2,7,9} = #{1,13,169,2197};

%e a(3537) = 28561: #{1,2,5,6,8} = #{1,13,169,2197,28561}.

%t Select[Range[1000],DivisorSigma[0,#]==Length[Union[IntegerDigits[#]]]&] (* _Harvey P. Dale_, May 20 2011 *)

%o (PARI) is(n)=numdiv(n)==#Set(digits(n)) \\ _Charles R Greathouse IV_, Feb 23 2017

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, Aug 09 2007