A132077 - OEIS

A132077

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

1, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 113, 131, 151, 169, 181, 191, 199, 211, 223, 227, 229, 233, 277, 289, 311, 313, 331, 337, 353, 361, 373, 383, 433, 443, 449, 499, 529, 557, 577, 599, 661, 677, 727, 733, 757

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

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

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

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

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

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

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

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

MATHEMATICA

Select[Range[1000], DivisorSigma[0, #]==Length[Union[IntegerDigits[#]]]&] (* Harvey P. Dale, May 20 2011 *)

PROG

(PARI) is(n)=numdiv(n)==#Set(digits(n)) \\ Charles R Greathouse IV, Feb 23 2017