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A132077 Numbers having in decimal representation exactly the same number of distinct digits as number of divisors. 1
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

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

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Last modified May 30 18:38 EDT 2020. Contains 334728 sequences. (Running on oeis4.)