1681

Number
$1681$ (one thousand six hundred and eighty-one) is:


 * $41^2$


 * The $41$st square number after $1, 4, 9, 16, 25, 36, \ldots, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600$:
 * $1681 = 41 \times 41$


 * The $36$th positive integer which cannot be expressed as the sum of a square and a prime:
 * $1, 10, 25, 34, 58, 64, 85, \ldots, 706, 730, 771, 784, 841, 1024, 1089, 1225, 1255, 1351, 1414, 1444, 1521, 1681, \ldots$