1225

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


 * 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 $1$, $3$, $6$, $10$, $15$, $\ldots$, $496$, $528$, $561$, $595$, $630$, $666$, $703$, $741$, $780$, $820$, $861$, $903$, $946$, $990$, $1035$, $1081$, $1128$:
 * $1225 = \displaystyle \sum_{k \mathop = 1}^{49} k = \dfrac {49 \times \left({49 + 1}\right)} 2$


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


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


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


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