650

Number
$650$ (six hundred and fifty) is:


 * $2 \times 5^2 \times 13$


 * The $11$th primitive abundant number after $20$, $70$, $88$, $104$, $272$, $304$, $368$, $464$, $550$, $572$:
 * $1 + 2 + 5 + 10 + 13 + 25 + 26 + 50 + 65 + 130 + 325 = 652 > 650$


 * The $12$th square pyramidal number after $1$, $5$, $14$, $30$, $55$, $91$, $140$, $204$, $285$, $385$, $506$:
 * $650 = \ds \sum_{k \mathop = 1}^{12} k^2 = \dfrac {12 \paren {12 + 1} \paren {2 \times 12 + 1} } 6$


 * The $15$th primitive semiperfect number after $6$, $20$, $28$, $88$, $104$, $272$, $304$, $350$, $368$, $464$, $490$, $496$, $550$, $572$:
 * $650 = 1 + 5 + 10 + 13 + 25 + 26 + 50 + 65 + 130 + 325$


 * The $24$th integer after $7$, $13$, $19$, $35$, $38$, $\ldots$, $223$, $253$, $285$, $305$, $350$, $380$, $410$, $475$, $487$, $570$ the decimal representation of whose square can be split into two parts which are each themselves square:
 * $650^2 = 422 \, 500$; $4 = 2^2$, $22 \, 500 = 150^2$

Also see