A132080 Numbers having in decimal representation no common digits with all their proper divisors.

2, 3, 4, 5, 6, 7, 8, 9, 23, 27, 29, 34, 37, 38, 43, 46, 47, 49, 53, 54, 56, 57, 58, 59, 67, 68, 69, 73, 76, 78, 79, 83, 86, 87, 89, 97, 223, 227, 229, 233, 239, 247, 249, 257, 259, 263, 267, 269, 277, 283, 289, 293, 307, 323, 329, 334, 337, 347, 349, 353, 356, 358, 359

Offset: 1

Author

Reinhard Zumkeller, Aug 09 2007

Keywords

• nonn
• base

Comments

A038603 is a subsequence.

Examples

			Proper divisors of a(20)=54: {1, 2, 3, 6, 9, 18, 27}
with set of digits {1,2,3,6,7,8,9} containing neither 4 nor 5.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Proper Divisor

Crossrefs

Subsequence of A052383.

Programs

Haskell

import Data.List (intersect)
a132080 n = a132080_list !! (n-1)
a132080_list = [x | x <- [2..], all null $
                    map (show x `intersect`) $ map show $ a027751_row x]
-- Reinhard Zumkeller, Oct 06 2012

Mathematica

Select[Range[2,359],ContainsNone[IntegerDigits[#],IntegerDigits/@Drop[Divisors[#],-1]//Flatten]&] (* James C. McMahon, Mar 03 2025 *)

PARI

is(n)=my(D=Set(digits(n))); fordiv(n,d, if(#setintersect(D, Set(digits(d))), return(d==n&&n>1))) \\ Charles R Greathouse IV, Dec 01 2013