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

1,2

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]

Links

Table of n, a(n) for n=1..28.

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

Adjacent sequences: A155002 A155003 A155004 * A155006 A155007 A155008

Keyword

base,nonn

Author

Reinhard Zumkeller, Jan 18 2009

Extensions

a(17)-a(28) from Robert G. Wilson v, Jan 23 2009

Status

approved