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 $25$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:
 * $1, 10, 25, 34, 58, 64, 85, \ldots, 706, 730, 771, 784, 841, 1024, 1089, 1225, \ldots$