A059436 Smallest number whose set of divisors contains each digit 0-9 at least n times.

108, 540, 1140, 1890, 3420, 5460, 7980, 11760, 16380, 23520, 23520, 23760, 38220, 38220, 41580, 41580, 41580, 71820, 71820, 71820, 83160, 83160, 83160, 124740, 124740, 143640, 166320, 166320, 249480, 249480, 249480, 249480, 311220, 335160, 415800, 415800, 415800, 415800, 415800, 415800

Offset: 1

Author

Erich Friedman, Feb 01 2001

Keywords

• base
• nonn
• nice

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000
• Erich Friedman, What's Special About This Number? (See entry 7980.)

Crossrefs

Cf. A027750; subsequence of A095050, A095048.

Programs

Haskell

import Data.List (group, sort)
a059436 n = head [x | x <- [1..],
   let dds = map length $ group $ sort $ concatMap show $ a027750_row x,
   minimum dds == n, length dds == 10]
-- Reinhard Zumkeller, Feb 04 2012

Mathematica

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 *)
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 *)

Extensions

More terms from David W. Wilson, Aug 31 2001

Offset corrected by R. J. Mathar, Jun 02 2010

a(10)-a(36) corrected by Giovanni Resta, May 15 2016

More terms from Harvey P. Dale, Mar 27 2024