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

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

Crossrefs

Sequence in context: A046064 A322274 A008365 * A235154 A045921 A296520

Adjacent sequences: A132074 A132075 A132076 * A132078 A132079 A132080

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 09 2007

Status

approved