Near-Perfect Number Tester
Tooling to search for k-near perfect numbers with a modified Sieve of Eratosthenes — written to produce evidence for a paper on 2-near perfect numbers.
2025
A near-perfect number misses its perfect target by a small, structured amount. Searching the form n = 2ᵏ × p² up to 10,000,000 turns up a tidy set:
| n | σ(n) | 2n | diff | Valid (d₁, d₂) combinations |
|---|---|---|---|---|
| 18 | 39 | 36 | 3 | +1 +2; +2 +1; +6 -3; +9 -6 |
| 36 | 91 | 72 | 19 | +1 +18; +18 +1 |
| 50 | 93 | 100 | -7 | -2 -5; -5 -2 |
| 196 | 399 | 392 | 7 | +14 -7 |
| 200 | 465 | 400 | 65 | +25 +40; +40 +25 |
| 2312 | 4605 | 4624 | -19 | -17 -2; -2 -17 |
| 15376 | 30783 | 30752 | 31 | +62 -31 |
| 1032256 | 2064639 | 2064512 | 127 | +254 -127 |
| 8454272 | 16908285 | 16908544 | -259 | -2 -257; -257 -2 |