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%I #5 Mar 15 2015 20:40:07
%S 1,10,12,110,120,1020,1200,1248,10250,11250,12480,31248,132600,124800,
%T 112500,312480,1248000,1312500,1125000,3124800,14437500,16250000,
%U 11250000,31248000,103125000,144375000,112500000,131250000
%N Smallest number having exactly n divisors that are contained in its decimal representation.
%C A121041(a(n)) = n and A121041(m) < n for m < a(n).
%C Conjecture: a(5+5n)=1125*10^n for n>0. [_Robert G. Wilson v_, Jan 23 2009]
%e a(4) = 110, A121041(110) = #{1, 10, 11, 110} = 4;
%e a(5) = 120, A121041(120) = #{1, 2, 12, 20, 120} = 5;
%e a(6) = 1020, A121041(1020) = #{1, 2, 10, 20, 102, 1020} = 6.
%t f[n_] := Block[{d = Divisors@ n, len = DivisorSigma[0, n], i = 1, c = 1, s = ToString@ n}, While[i < len, If[ StringMatchQ[s, "*" <> ToString[d[[i]]] <> "*"], c++ ] ; i++ ]; c]; t = Table[0, {30}]; Do[ a = f[n]; If[ t[[a]] == 0, t[[a]] = n; Print[{a, n}]], {n, 2*10^8}] (* _Robert G. Wilson v_, Jan 23 2009 *)
%K base,nonn
%O 1,2
%A _Reinhard Zumkeller_, Jan 18 2009
%E a(17)-a(28) from _Robert G. Wilson v_, Jan 23 2009
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