All positive divisors of N (except 1) contain the digit d = 1,2,…,9

 
 
Here are the smallest values for   N   I could find:
 

121   has 3 divisors :     1,   11,   121

All divisors of   121   contain the digit 1

 

254   has 4 divisors:     1,   2,   127,   254

Divisors (2,   127,   254) contain the digit 2

 

39   has 4 divisors:     1,   3,   13,   39

Divisors   (3,   13,   39)   contain the digit 3

 

1849   has 3 divisors:     1,   43,   1849

All divisors of   1849   (with the exclusion of 1) contain the digit 4

 

25   has 3 divisors:     1,   5,   25

Divisors   (5,   25) contain the digit 5

 

16043   has 4 divisors:     1,   61,   263,   16043

All divisors of   16043   (with the exclusion of 1) contain the digit 6

 

497   has 4 divisors:     1,   7,   71,   497

Divisors   (7,   71,   497)   contain the digit 7

 

6889   has 3 divisors:     1,   83,   6889

All divisors of   6889   (with the exclusion of 1) contain the digit 8

 

1691   has 4 divisors:     1,   19,   89,   1691

Divisors   (19,   89,   1691)   contain the digit 9

 

Double digits:

10201   has 3 divisors:     1,   101,   10201

Divisors   (101,   10201)   contain 10

171121   has 4 divisors:     1,   211,   811,   171121

Divisors   (211,   811,   171121)   contain 11

16129   has 3 divisors:     1,   127,   16129

Divisors   (127,   16129)   contain 12

 
Other results:

Digit 1 :

1859   :     1,   11,   13,   143,   169,   1859

Digit 2 :

32258   :     1,   2,   127,   254,   16129,   32258

Digit 3 :

34917   :     1,   3,   103,   113,   309,   339,   11639,   34917

Digit 4 :

Digit 5 :

75815   :     1,   5,   59,   257,   295,   1285,   15163,   75815

Digit 6 :

Digit 7 :

5767   :     1,   73,   79,   5767
53179   :     1,   7,   71,   107,   497,   749,   7597,   53179

Digit 8 :

7387   :     1,   83,   89,   7387

Digit 9 :

150499   :     1,   19,   89,   1691,   7921,   150499

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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