27700 is a product of a power of 2, a 4k+1 prime raised to the power 2 and a 4k+1 prime and so it can be expressed as a sum of two squares in three different ways viz 12^2+166^2 and 58^2+156^2 and 90^2+140^2.

27700 is a member of A220139: the highest value of the Collatz iteration (3x+1) starting at a(n-1) + 1, with a(1) = 1. The trajectory of 9233 is as follows:

[9233, 27700, 13850, 6925, 20776, 10388, 5194, 2597, 7792, 3896, 1948, 974, 487, 1462, 731, 2194, 1097, 3292, 1646, 823, 2470, 1235, 3706, 1853, 5560, 2780, 1390, 695, 2086, 1043, 3130, 1565, 4696, 2348, 1174, 587, 1762, 881, 2644, 1322, 661, 1984, 992, 496, 248, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1]

27700 is an abundant and pseudoperfect but NOT Zumkeller number.

27700 can be rendered as a digit equation as follows:

2 * 7 * 7 * 0 = 0