> For the complete documentation index, see [llms.txt](https://trizen.gitbook.io/sidef-lang/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://trizen.gitbook.io/sidef-lang/programming_tasks/a/abundant_odd_numbers.md).

# Abundant odd numbers

```ruby
func is_abundant(n) {
    n.sigma > 2*n
}

func odd_abundants (from = 1) {
     from =  (from + 2)//3
     from += (from%2 - 1)
     3*from .. Inf `by` 6 -> lazy.grep(is_abundant)
}

say         " Index |      Number | proper divisor sum"
const sep = "-------+-------------+-------------------\n"
const fstr = "%6s | %11s | %11s\n"

print sep

odd_abundants().first(25).each_kv {|k,n|
    printf(fstr, k+1, n, n.sigma-n)
}

with (odd_abundants().nth(1000)) {|n|
    printf(sep + fstr, 1000, n, n.sigma-n)
}

with(odd_abundants(1e9).first) {|n|
    printf(sep + fstr, '***', n, n.sigma-n)
}
```

## Output:

```
 Index |      Number | proper divisor sum
-------+-------------+-------------------
     1 |         945 |         975
     2 |        1575 |        1649
     3 |        2205 |        2241
     4 |        2835 |        2973
     5 |        3465 |        4023
     6 |        4095 |        4641
     7 |        4725 |        5195
     8 |        5355 |        5877
     9 |        5775 |        6129
    10 |        5985 |        6495
    11 |        6435 |        6669
    12 |        6615 |        7065
    13 |        6825 |        7063
    14 |        7245 |        7731
    15 |        7425 |        7455
    16 |        7875 |        8349
    17 |        8085 |        8331
    18 |        8415 |        8433
    19 |        8505 |        8967
    20 |        8925 |        8931
    21 |        9135 |        9585
    22 |        9555 |        9597
    23 |        9765 |       10203
    24 |       10395 |       12645
    25 |       11025 |       11946
-------+-------------+-------------------
  1000 |      492975 |      519361
-------+-------------+-------------------
   *** |  1000000575 |  1083561009
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://trizen.gitbook.io/sidef-lang/programming_tasks/a/abundant_odd_numbers.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.