497

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Number

$497$ (four hundred and ninety-seven) is:

$7 \times 71$

The $1$st counterexample to Greenwood's Conjecture:

$497 = T_{31} + 1 = \dfrac {31 \times \paren {31 + 1} } 2 + 1$ but is not prime

The $2$nd number such that the result when adding $2$ is the reversal of when multiplying by $2$:

$497 + 2 = 499$; $497 \times 2 = 994$

The $26$th number whose divisor sum is square:

$\map {\sigma_1} {497} = 576 = 24^2$

Also see

• Greenwood's Conjecture

• Previous  ... Next: Numbers which Multiplied by 2 are the Reverse of when Added to 2
• Previous  ... Next: Numbers whose Divisor Sum is Square

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $496$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $496$