|
|
A095050
|
|
Numbers such that all ten digits are needed to write all positive divisors in decimal representation.
|
|
18
|
|
|
108, 216, 270, 304, 306, 312, 324, 360, 380, 406, 432, 450, 504, 540, 570, 608, 612, 624, 630, 648, 654, 702, 708, 714, 720, 728, 756, 760, 780, 810, 812, 864, 870, 900, 910, 912, 918, 924, 936, 945, 954, 972, 980, 1008, 1014, 1026, 1032, 1036, 1038
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Once a number is in the sequence, then all its multiples will be there too. The list of primitive terms begin: 108, 270, 304, 306, 312, 360, 380, ... - Michel Marcus, Jun 20 2014
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
Divisors of 108 are: [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108] where all digits can be found.
|
|
MAPLE
|
q:= n-> is({$0..9}=map(x-> convert(x, base, 10)[], numtheory[divisors](n))):
|
|
MATHEMATICA
|
Select[Range@2000, 1+Union@@IntegerDigits@Divisors@# == Range@10 &] (* Hans Rudolf Widmer, Oct 28 2021 *)
|
|
PROG
|
(Haskell)
import Data.List (elemIndices)
a095050 n = a095050_list !! (n-1)
a095050_list = map (+ 1) $ elemIndices 10 $ map a095048 [1..]
(PARI) isok(m)=my(d=divisors(m), v=[1]); for (k=2, #d, v = Set(concat(v, digits(d[k]))); if (#v == 10, return (1)); ); #v == 10; \\ Michel Marcus, May 01 2020
(Python)
from sympy import divisors
def ok(n):
digits_used = set()
for d in divisors(n):
digits_used |= set(str(d))
return len(digits_used) == 10
|
|
CROSSREFS
|
Cf. A243543 (the smallest number m whose list of divisors contains n distinct digits).
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|