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 its 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*/
- = 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>
- 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