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%I #35 Mar 27 2024 17:33:26
%S 108,540,1140,1890,3420,5460,7980,11760,16380,23520,23520,23760,38220,
%T 38220,41580,41580,41580,71820,71820,71820,83160,83160,83160,124740,
%U 124740,143640,166320,166320,249480,249480,249480,249480,311220,335160,415800,415800,415800,415800,415800,415800
%N Smallest number whose set of divisors contains each digit 0-9 at least n times.
%H Giovanni Resta, <a href="/A059436/b059436.txt">Table of n, a(n) for n = 1..1000</a>
%H Erich Friedman, <a href="https://erich-friedman.github.io/numbers.html">What's Special About This Number?</a> (See entry 7980.)
%e The divisors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540 and every digit appears at least twice in this list.
%t T = 0*Range[25]; Do[d = Last /@ Tally@ Flatten[ IntegerDigits /@ Divisors@ n]; If[Length@d == 10, m = Min[25, d]; While[m > 0 && (T[[m]] == 0 || n < T[[m]]), T[[m--]] = n]], {n, 125000}]; T (* _Giovanni Resta_, May 15 2016 *)
%t sded[n_]:=With[{fid=Flatten[IntegerDigits/@Divisors[n]]},If[Length[Union[fid]]==10,{n,Min[ Tally[fid][[;;,2]]]},Nothing]]; Table[SelectFirst[sded/@Range[500000],#[[2]]>k&],{k,0,39}][[;;,1]] (* _Harvey P. Dale_, Mar 27 2024 *)
%o (Haskell)
%o import Data.List (group, sort)
%o a059436 n = head [x | x <- [1..],
%o let dds = map length $ group $ sort $ concatMap show $ a027750_row x,
%o minimum dds == n, length dds == 10]
%o -- _Reinhard Zumkeller_, Feb 04 2012
%Y Cf. A027750; subsequence of A095050, A095048.
%K base,nonn,nice
%O 1,1
%A _Erich Friedman_, Feb 01 2001
%E More terms from _David W. Wilson_, Aug 31 2001
%E Offset corrected by _R. J. Mathar_, Jun 02 2010
%E a(10)-a(36) corrected by _Giovanni Resta_, May 15 2016
%E More terms from _Harvey P. Dale_, Mar 27 2024
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