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A155005
Smallest number having exactly n divisors that are contained in its decimal representation.
1
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
1,2
COMMENTS
A121041(a(n)) = n and A121041(m) < n for m < a(n).
Conjecture: a(5+5n)=1125*10^n for n>0. [Robert G. Wilson v, Jan 23 2009]
EXAMPLE
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.
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 *)
CROSSREFS
Sequence in context: A116118 A038314 A119225 * A219213 A078217 A359356
KEYWORD
base,nonn
AUTHOR
Reinhard Zumkeller, Jan 18 2009
EXTENSIONS
a(17)-a(28) from Robert G. Wilson v, Jan 23 2009
STATUS
approved