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Table of positive integers as sums of five positive squares
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With a few exceptions (see A047701), all positive integers can be expressed as the sum of five positive squares (and some of them in more than one way, such as the numbers in A193143). Hence this table of positive integers as sums of five positive squares. The squares are listed in descending order.
| 5 | 12 + 12 + 12 + 12 + 12 |
| 6 | N/A |
| 7 | N/A |
| 8 | 22 + 12 + 12 + 12 + 12 |
| 9 | N/A |
| 10 | N/A |
| 11 | 22 + 22 + 12 + 12 + 12 |
| 12 | N/A |
| 13 | 32 + 12 + 12 + 12 + 12 |
| 14 | 22 + 22 + 22 + 12 + 12 |
| 15 | N/A |
| 16 | 32 + 22 + 12 + 12 + 12 |
| 17 | 22 + 22 + 22 + 22 + 12 |
| 18 | N/A |
| 19 | 32 + 22 + 22 + 12 + 12 |
| 20 | 22 + 22 + 22 + 22 + 22 |
| 21 | 32 + 32 + 12 + 12 + 12 |
| 22 | 32 + 22 + 22 + 22 + 12 |
| 23 | 42 + 22 + 12 + 12 + 12 |
| 24 | 32 + 32 + 22 + 12 + 12 |
| 25 | 32 + 22 + 22 + 22 + 22 |
| 26 | 42 + 22 + 22 + 12 + 12 |
| 27 | 32 + 32 + 22 + 22 + 12 |
| 28 | 42 + 32 + 12 + 12 + 12 |
| 29 | 52 + 12 + 12 + 12 + 12 |
| 30 | 32 + 32 + 22 + 22 + 22 |
| 31 | 42 + 32 + 22 + 12 + 12 |
| 32 | 32 + 32 + 32 + 22 + 12 |
| 33 | N/A |
| 34 | 42 + 32 + 22 + 22 + 12 |
| 35 | 32 + 32 + 32 + 22 + 22 |
| 36 | 42 + 32 + 32 + 12 + 12 |
| 37 | 32 + 32 + 32 + 32 + 12 |
| 38 | 52 + 22 + 22 + 22 + 12 |
| 39 | 42 + 32 + 32 + 22 + 12 |
| 40 | 32 + 32 + 32 + 32 + 22 |
| 41 | 52 + 22 + 22 + 22 + 22 |
WHEN COMPLETED, THIS TABLE WILL GO UP TO 169, AND THE REASON WILL ALSO BE GIVEN AS TO WHY IT'S NOT NECESSARY TO GO FURTHER.
