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A093785 Numbers that are divisible by every digit in their Roman numeral representation.

%I A093785 #26 Feb 16 2025 08:32:53
%S A093785 1,2,3,5,10,20,30,50,100,200,300,500,1000,2000,3000
%N A093785 Numbers that are divisible by every digit in their Roman numeral representation.
%C A093785 The sequence contains only values less than 4000, see A078715 for a discussion on the Roman 4M-problem.
%H A093785 Stephanus Gibbs, <a href="http://www.softhawkway.com/rcalc.htm">Roman Numeral and Date Conversion</a>
%H A093785 Gerard Schildberger, <a href="/A006968/a006968.txt">The first 3999 numbers in Roman numerals</a>
%H A093785 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RomanNumerals.html">Roman Numerals</a>
%H A093785 Wikipedia, <a href="http://en.wikipedia.org/wiki/Roman_numerals">Roman numerals</a>
%e A093785 I, II, III, V, X, XX, XXX, L, C, CC, CCC, D, M, MM, MMM.
%o A093785 (Haskell)
%o A093785 a093785 n = a093785_list !! (n-1)
%o A093785 a093785_list = filter p [1..3999] where
%o A093785    p v = q $ a061493 v where
%o A093785      q w = w == 0 || v `mod` ([0,1,5,10,50,100,500,1000] !! d') == 0 && q w'
%o A093785           where  (w',d) = divMod w 10; d' = fromInteger d
%o A093785 -- _Reinhard Zumkeller_, Apr 14 2013
%Y A093785 Cf. A034838.
%Y A093785 Cf. A061493.
%K A093785 nonn,base,fini,full
%O A093785 1,2
%A A093785 _Reinhard Zumkeller_, May 17 2004