A155005 Smallest number having exactly n divisors that are contained in its decimal representation.
1, 10, 12, 110, 120, 1020, 1200, 1248, 10250, 11250, 12480, 31248, 132600, 124800, 112500, 312480, 1248000, 1312500, 1125000, 3124800, 14437500, 16250000, 11250000, 31248000, 103125000, 144375000, 112500000, 131250000
Offset: 1
Examples
a(4) = 110, A121041(110) = #{1, 10, 11, 110} = 4;
a(5) = 120, A121041(120) = #{1, 2, 12, 20, 120} = 5;
a(6) = 1020, A121041(1020) = #{1, 2, 10, 20, 102, 1020} = 6.
Programs
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Mathematica
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 *) dcdr[n_]:=Count[Divisors[n],?(SequenceCount[IntegerDigits[n],IntegerDigits[#]]>0&)]; DeleteDuplicates[Table[{n,dcdr[n]},{n,1313*10^5}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale, Feb 04 2025 *)
Extensions
a(17)-a(28) from Robert G. Wilson v, Jan 23 2009
Comments