4900

Number
$4900$ (four thousand, nine hundred) is:


 * $2^2 \times 5^2 \times 7^2$


 * The only square pyramidal number which is also square:
 * $4900 = 70^2 = \displaystyle \sum_{k \mathop = 1}^{24} k^2 = \dfrac {24 \paren {24 + 1} \paren {2 \times 24 + 1} } 6$


 * The $9$th square whose decimal representation can be split into two parts which are each themselves square:
 * $4900 = 70^2$; $4 = 2^2$, $900 = 30^2$


 * The $24$th square pyramidal number after $1$, $5$, $14$, $30$, $55$, $\ldots$, $1015$, $1240$, $1496$, $1785$, $2109$, $2470$, $2870$, $3311$, $3795$, $4324$:
 * $4900 = \displaystyle \sum_{k \mathop = 1}^{24} k^2 = \dfrac {24 \paren {24 + 1} \paren {2 \times 24 + 1} } 6$


 * The $27$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $\ldots$, $1936$, $2304$, $2704$, $2916$, $3136$, $3600$, $3844$, $4096$, $4356$, $4624$ to be the $\sigma$ (sigma) value of some (strictly) positive integer:
 * $4900 = \map \sigma {4537}$


 * The $70$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $4096$, $4225$, $4356$, $4489$, $4624$, $4761$:
 * $4900 = 70 \times 70$

Also see

 * Square Pyramidal Number also Square