Multiply Perfect Number of Order 8/Mistake
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Source Work
1986: David Wells: Curious and Interesting Numbers:
- The Dictionary
- $120$
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $120$
Mistake
- One of the smallest [multiply perfect numbers] of order $8$ was discovered by Alan L. Brown, an American 'human computer': $2 \times 3^{23} \times 5^9 \times 7^{12} \times 11^3 \times 13^3 \times 17^2 \times$
- $19^2 \times 23 \times 29^2 \times 31^2 \times 37 \times 41 \times 53 \times 61 \times 67^2 \times 71^2 \times 73 \times 83$
- $\times 89 \times 103 \times 127 \times 131 \times 149 \times 211 \times 307 \times 331 \times 463 \times 521$
- $\times 683 \times 709 \times 1279 \times 2141 \times 2557 \times 5113 \times 6481 \times 10,429$
- $\times 20,857 \times 110,563 \times 599,479 \times 16,148,168,401$.
The multiplicity of $2$ has been omitted: the expression should read $2^{65} \times 3^{23} \times 5^9 \ldots$
In David Wells' defence, he merely propagates the error as it appears in Richard K. Guy's Unsolved Problems in Number Theory, 2nd ed. of $1994$.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $120$
- 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $120$