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

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..1000

Erich Friedman, What's Special About This Number? (See entry 7980.)

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A027750; subsequence of A095050, A095048.

Sequence in context: A251270 A255083 A063880 * A233685 A160919 A129027

Adjacent sequences: A059433 A059434 A059435 * A059437 A059438 A059439

Keyword

base,nonn,nice

Author

Erich Friedman, Feb 01 2001

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

Status

approved