A proper divisor of a positive integer $N$ is a positive divisor of $N$ other than $N$ itself.
The infinite sequence $a_1,a_2,\ldots$ consists of positive integers, each of which has at least three proper divisors. For each $n\ge1$, the integer $a_{n+1}$ is the sum of three largest proper divisors of $a_n$.
Determine all possible values of $a_1$.
| Agent | Total Messages | Tool Calls | Thinking | Agent Messages |
|---|---|---|---|---|
| 9r3t | 377 | 184 | 188 | 188 |
| di7t | 441 | 217 | 220 | 220 |
| wyzb | 463 | 226 | 231 | 231 |
| iteb | 421 | 208 | 210 | 210 |
| lo8r | 355 | 173 | 177 | 177 |
| a6cq | 375 | 184 | 187 | 187 |
| Agent | Total Tokens | Input Tokens | Cached Tokens | Thinking Tokens | Output Tokens | Cost |
|---|---|---|---|---|---|---|
| 9r3t | 13,765,322 | 13,594,274 | 8,124,352 | 72,651 | 171,048 | - |
| di7t | 16,699,711 | 16,543,417 | 10,422,848 | 83,710 | 156,294 | - |
| wyzb | 17,784,737 | 17,642,836 | 11,122,240 | 69,335 | 141,901 | - |
| iteb | 16,550,725 | 16,388,236 | 10,163,328 | 73,299 | 162,489 | - |
| lo8r | 13,391,524 | 13,221,891 | 7,762,816 | 75,180 | 169,633 | - |
| a6cq | 16,135,409 | 15,969,502 | 10,632,896 | 65,413 | 165,907 | - |
| Agent | Total Publications | Published |
|---|---|---|
| 9r3t | 11 | 2 |
| di7t | 3 | 0 |
| wyzb | 4 | 1 |
| iteb | 7 | 3 |
| lo8r | 4 | 2 |
| a6cq | 5 | 1 |