All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Neighbors (Posted on 2014-04-18) Difficulty: 2 of 5
Find the smallest integer n such that both n-1 and n+1 have the same number of divisors as n.
Bonus task: List few additional numbers with said feature.

See The Solution Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution | Comment 4 of 8 |


DefDbl A-Z
Dim fct(20, 1)


Private Sub Form_Load()
 Text1.Text = ""

   For n = 2 To 10000
     a = b: b = c
     f = factor(n)
     nf = 1
     For i = 1 To f
      nf = nf * (fct(i, 1) + 1)
     Next
     c = nf
     If a = b And b = c Then
       Text1.Text = Text1.Text & Str(n - 1) & Str(c) & Chr(13) & Chr(10)
     End If
   Next
 
End Sub

Function factor(num)
 diffCt = 0: good = 1
 n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
 If limit <> Int(limit) Then limit = Int(limit + 1)
 dv = 2: GoSub DivideIt
 dv = 3: GoSub DivideIt
 dv = 5: GoSub DivideIt
 dv = 7
 Do Until dv > limit
   GoSub DivideIt: dv = dv + 4 '11
   GoSub DivideIt: dv = dv + 2 '13
   GoSub DivideIt: dv = dv + 4 '17
   GoSub DivideIt: dv = dv + 2 '19
   GoSub DivideIt: dv = dv + 4 '23
   GoSub DivideIt: dv = dv + 6 '29
   GoSub DivideIt: dv = dv + 2 '31
   GoSub DivideIt: dv = dv + 6 '37
   If INKEY$ = Chr$(27) Then s$ = Chr$(27): Exit Function
 Loop
 If n > 1 Then diffCt = diffCt + 1: fct(diffCt, 0) = n: fct(diffCt, 1) = 1
 factor = diffCt
 Exit Function

DivideIt:
 cnt = 0
 Do
  q = Int(n / dv)
  If q * dv = n And n > 0 Then
    n = q: cnt = cnt + 1: If n > 0 Then limit = Sqr(n) Else limit = 0
    If limit <> Int(limit) Then limit = Int(limit + 1)
   Else
    Exit Do
  End If
 Loop
 If cnt > 0 Then
   diffCt = diffCt + 1
   fct(diffCt, 0) = dv
   fct(diffCt, 1) = cnt
 End If
 Return
End Function

Finds the following values for n under 10,000, with the number of divisors of n, which, per the instructions, is the same as for n-1 and n+1. The number of factors includes counting 1 and the number itself.

 34 4
 86 4
 94 4
 142 4
 202 4
 214 4
 218 4
 231 8
 243 6
 244 6
 302 4
 375 8
 394 4
 446 4
 604 6
 634 4
 664 8
 698 4
 903 8
 922 4
 1042 4
 1106 8
 1138 4
 1262 4
 1275 12
 1310 8
 1335 8
 1346 4
 1402 4
 1642 4
 1762 4
 1833 8
 1838 4
 1886 8
 1894 4
 1925 12
 1942 4
 1982 4
 2014 8
 2055 8
 2102 4
 2134 8
 2182 4
 2218 4
 2265 8
 2306 4
 2344 8
 2362 4
 2434 4
 2462 4
 2505 8
 2518 4
 2524 6
 2642 4
 2666 8
 2697 8
 2722 4
 2734 4
 2937 8
 3098 4
 3111 8
 3386 4
 3602 4
 3656 8
 3657 8
 3694 4
 3730 8
 3866 4
 3902 4
 3958 4
 4204 6
 4286 4
 4402 8
 4414 4
 4504 8
 4505 8
 4534 4
 4594 4
 4615 8
 4670 8
 4696 8
 4808 8
 4882 4
 4924 6
 5134 8
 5602 4
 5722 4
 5854 4
 5863 8
 5944 8
 5945 8
 5998 4
 6055 8
 6062 8
 6153 8
 6158 4
 6183 8
 6214 8
 6306 8
 6458 4
 6478 8
 6585 8
 6854 8
 6855 8
 6873 8
 6986 8
 7114 4
 7142 4
 7166 4
 7234 4
 7257 8
 7258 8
 7342 4
 7402 4
 7443 6
 7527 8
 7862 4
 7954 8
 7978 4
 8158 4
 8186 4
 8225 12
 8258 4
 8295 16
 8393 8
 8394 8
 8402 4
 8458 4
 8534 8
 8696 8
 8786 8
 8823 8
 8914 4
 8937 8
 9122 4
 9163 12
 9214 8
 9368 8
 9369 8
 9454 8
 9694 8
 9705 8
 9754 4
 9822 8
 9831 8
 9878 8
 9910 8
 9938 4
 9986 4


  Posted by Charlie on 2014-04-18 13:02:09
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information