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

%I A132080 #16 Mar 04 2025 07:34:27
%S A132080 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,
%T A132080 68,69,73,76,78,79,83,86,87,89,97,223,227,229,233,239,247,249,257,259,
%U A132080 263,267,269,277,283,289,293,307,323,329,334,337,347,349,353,356,358,359
%N A132080 Numbers having in decimal representation no common digits with all their proper divisors.
%C A132080 A038603 is a subsequence.
%H A132080 Reinhard Zumkeller, <a href="/A132080/b132080.txt">Table of n, a(n) for n = 1..10000</a>
%H A132080 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ProperDivisor.html">Proper Divisor</a>
%e A132080 Proper divisors of a(20)=54: {1, 2, 3, 6, 9, 18, 27}
%e A132080 with set of digits {1,2,3,6,7,8,9} containing neither 4 nor 5.
%t A132080 Select[Range[2,359],ContainsNone[IntegerDigits[#],IntegerDigits/@Drop[Divisors[#],-1]//Flatten]&] (* _James C. McMahon_, Mar 03 2025 *)
%o A132080 (Haskell)
%o A132080 import Data.List (intersect)
%o A132080 a132080 n = a132080_list !! (n-1)
%o A132080 a132080_list = [x | x <- [2..], all null $
%o A132080                     map (show x `intersect`) $ map show $ a027751_row x]
%o A132080 -- _Reinhard Zumkeller_, Oct 06 2012
%o A132080 (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
%Y A132080 Subsequence of A052383.
%K A132080 nonn,base
%O A132080 1,1
%A A132080 _Reinhard Zumkeller_, Aug 09 2007