4900

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Number

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

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

The only square pyramidal number which is also square:

$4900 = 70^2 = \ds \sum_{k \mathop = 1}^{24} k^2 = \dfrac {24 \paren {24 + 1} \paren {2 \times 24 + 1} } 6$

The $9$th square after $49$, $169$, $361$, $1225$, $1444$, $1681$, $3249$, $4225$ 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 $1$, $5$, $14$, $30$, $55$, $\ldots$, $1015$, $1240$, $1496$, $1785$, $2109$, $2470$, $2870$, $3311$, $3795$, $4324$:

$4900 = \ds \sum_{k \mathop = 1}^{24} k^2 = \dfrac {24 \paren {24 + 1} \paren {2 \times 24 + 1} } 6$

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 divisor sum value of some (strictly) positive integer:

$4900 = \map {\sigma_1} {4537}$

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

• Previous  ... Next: Squares whose Digits can be Separated into 2 other Squares
• Previous  ... Next: Square Pyramidal Number
• Previous  ... Next: Square Numbers which are Divisor Sum values
• Previous  ... Next: Square Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $4900$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $4900$