This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(9) = 54 because 54 is the smallest number whose list of divisors contains 9 distinct digits; the list of divisors of 54: (1, 2, 3, 6, 9, 18, 27, 54) contains 9 distinct digits (1, 2, 3, 4, 5, 6, 7, 8, 9).
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.
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
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 *)
Select[Range[12000],Length[Union[Flatten[IntegerDigits/@Divisors[#]]]]<3&] (* Harvey P. Dale, May 03 2022 *)
select( {is_A206159(n)=#Set(concat([digits(d)|d<-divisors(n)]))<3}, [1..10^4]) \\ M. F. Hasler, May 02 2022
from sympy import divisors
def ok(n):
digits_used = set()
for d in divisors(n, generator=True):
digits_used |= set(str(d))
if len(digits_used) > 2: return False
return True
print([k for k in range(1, 9000) if ok(k)]) # Michael S. Branicky, May 02 2022
Set of non-divisors of n=12: {5,7,8,9,10,11}, therefore
a(12)=#{0,1,5,7,8,9}=6.
Table[Length[Union[Flatten[IntegerDigits/@Complement[Range[n],Divisors[ n]]]]],{n,80}] (* Harvey P. Dale, Jan 06 2019 *)
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