Abundant odd numbers

Abundant odd numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

n is Nice number if it's sum of the factors is greater than n.

REXX

<lang rexx>/*REXX pgm displays N nice numbers, where nice #'s are whose sum of its factors > #. */ parse arg N . /*obtain optional arguments from the CL*/ if N== | N=="," then N= 25 /*Not specified? Then use the default.*/ w= length(N); ww= w+ w /*used for aligning the columnar output*/

1. = 0 /*count of nice numbers (so far). */

     do j=1  until #>=N;     $=sigma(j)         /*get sigma for an integer.            */
     if $<=j  then iterate                      /*sigma  +  J ?    Then ignore it.     */
     #= # + 1
     say 'nice number '   right(#,w)   " is:"   right(j,ww)',     sigma is:'  right($,ww)
     end  /*j*/

exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sigma: procedure; parse arg x; if x<2 then return 0; odd= x // 2 /* // ◄──remainder.*/

      s= 1                                      /* [↓]  only use  EVEN or ODD integers.*/
            do j=2+odd  by 1+odd  while j*j<x   /*divide by all integers up to  √x.    */
            if x//j==0  then  s= s + j +  x%j   /*add the two divisors to (sigma) sum. */
            end   /*j*/                         /* [↑]  %  is the REXX integer division*/
                                                /* [↓]  adjust for a square.       ___ */
      if j*j==x  then  return s + j             /*Was  X  a square?   If so, add  √ x  */
                       return s                 /*return (sigma) sum of the divisors.  */</lang>

output   when using the default input:

nice number   1  is:   12,     sigma is:   16
nice number   2  is:   18,     sigma is:   21
nice number   3  is:   20,     sigma is:   22
nice number   4  is:   24,     sigma is:   36
nice number   5  is:   30,     sigma is:   42
nice number   6  is:   36,     sigma is:   55
nice number   7  is:   40,     sigma is:   50
nice number   8  is:   42,     sigma is:   54
nice number   9  is:   48,     sigma is:   76
nice number  10  is:   54,     sigma is:   66
nice number  11  is:   56,     sigma is:   64
nice number  12  is:   60,     sigma is:  108
nice number  13  is:   66,     sigma is:   78
nice number  14  is:   70,     sigma is:   74
nice number  15  is:   72,     sigma is:  123
nice number  16  is:   78,     sigma is:   90
nice number  17  is:   80,     sigma is:  106
nice number  18  is:   84,     sigma is:  140
nice number  19  is:   88,     sigma is:   92
nice number  20  is:   90,     sigma is:  144
nice number  21  is:   96,     sigma is:  156
nice number  22  is:  100,     sigma is:  117
nice number  23  is:  102,     sigma is:  114
nice number  24  is:  104,     sigma is:  106
nice number  25  is:  108,     sigma is:  172

Ring

<lang ring>

1. Project: Nice numbers

max = 25 nr = 0 m = 1 check = 0 index = 0 while true

     nice(m)
     if check = 1
        nr = nr + 1
     ok
     if nr = max
        exit
     ok
     m = m + 1

end

func nice(n)

    check = 0
    nArray = []
    for i = 1 to n - 1
        if n % i = 0
           add(nArray,i)
        ok
    next
    sum = 0
    for p = 1 to len(nArray)
        sum = sum + nArray[p]
    next
    if sum > n
       check = 1
       index = index + 1
       showArray(n,nArray,sum,index)
    ok

func showArray(n,nArray,sum,index)

    see string(index) + ". " + string(n) + " => "
    for m = 1 to len(nArray)
        if m < len(nArray)
           see string(nArray[m]) + " + "
        else
           see string(nArray[m]) + " = " + string(sum) + " > " + string(n) + nl
        ok
    next

</lang>

Output:

1. 12 => 1 + 2 + 3 + 4 + 6 = 16 > 12
2. 18 => 1 + 2 + 3 + 6 + 9 = 21 > 18
3. 20 => 1 + 2 + 4 + 5 + 10 = 22 > 20
4. 24 => 1 + 2 + 3 + 4 + 6 + 8 + 12 = 36 > 24
5. 30 => 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42 > 30
6. 36 => 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55 > 36
7. 40 => 1 + 2 + 4 + 5 + 8 + 10 + 20 = 50 > 40
8. 42 => 1 + 2 + 3 + 6 + 7 + 14 + 21 = 54 > 42
9. 48 => 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 = 76 > 48
10. 54 => 1 + 2 + 3 + 6 + 9 + 18 + 27 = 66 > 54
11. 56 => 1 + 2 + 4 + 7 + 8 + 14 + 28 = 64 > 56
12. 60 => 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 = 108 > 60
13. 66 => 1 + 2 + 3 + 6 + 11 + 22 + 33 = 78 > 66
14. 70 => 1 + 2 + 5 + 7 + 10 + 14 + 35 = 74 > 70
15. 72 => 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 = 123 > 72
16. 78 => 1 + 2 + 3 + 6 + 13 + 26 + 39 = 90 > 78
17. 80 => 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 40 = 106 > 80
18. 84 => 1 + 2 + 3 + 4 + 6 + 7 + 12 + 14 + 21 + 28 + 42 = 140 > 84
19. 88 => 1 + 2 + 4 + 8 + 11 + 22 + 44 = 92 > 88
20. 90 => 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 = 144 > 90
21. 96 => 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 = 156 > 96
22. 100 => 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 = 117 > 100
23. 102 => 1 + 2 + 3 + 6 + 17 + 34 + 51 = 114 > 102
24. 104 => 1 + 2 + 4 + 8 + 13 + 26 + 52 = 106 > 104
25. 108 => 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 = 172 > 108