1225

Number
$1225$ (one thousand, two hundred and twenty-five) is:
 * $5^2 \times 7^2$


 * The $2$nd square number after $1$ which can be expressed as the sum of a sequence of odd cubes from $1$:
 * $1225 = 35^2 = 1^3 + 3^3 + 5^3 + 7^3 + 9^3$


 * The $3$rd number after $1$, $36$ to be both square and triangular:
 * $1225 = 35^2 = \dfrac {49 \times \paren {49 + 1} } 2$


 * The $4$th hexamorphic number after $1$, $45$, $66$:
 * $1225 = H_{25}$


 * The $4$th square whose decimal representation can be split into two parts which are each themselves square:
 * $1225 = 35^2$; $1 = 1^2$, $225 = 15^2$


 * The total of all the entries in a magic square of order $7$, after $1$, $(10)$, $45$, $136$, $325$, $666$:
 * $1225 = \displaystyle \sum_{k \mathop = 1}^{7^2} k = \dfrac {7^2 \paren {7^2 + 1} } 2$


 * The $25$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$, $1035$, $1128$:
 * $1225 = \displaystyle \sum_{k \mathop = 1}^{25} \paren {4 k - 3} = 25 \paren {2 \times 25 - 1}$


 * The $30$th positive integer which cannot be expressed as the sum of a square and a prime:
 * $1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $706$, $730$, $771$, $784$, $841$, $1024$, $1089$, $1225$, $\ldots$


 * The $35$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $625$, $676$, $729$, $784$, $841$, $900$, $961$, $1024$, $1089$, $1156$:
 * $1225 = 35 \times 35$


 * The $49$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $496$, $528$, $561$, $595$, $630$, $666$, $703$, $741$, $780$, $820$, $861$, $903$, $946$, $990$, $1035$, $1081$, $1128$, $1176$:
 * $1225 = \displaystyle \sum_{k \mathop = 1}^{49} k = \dfrac {49 \times \paren {49 + 1} } 2$