27521 is a product of three 4k+1 primes and can therefore be expressed as the sum of two squares in four different ways, namely as the sum of the squares of the following number pairs:(25, 164), (40,161), (89, 140), (95, 136).

27521 is a number with an arithmetical root (8) different to that of its prime factors, all of which have different digital roots (1, 2 and 4). See entry for 27303.

The sequence members from 27521 to 4000 are:

27521, 27537, 27546, 27582, 27591, 27618, 27638, 27683, 27713, 27726, 27745, 27789, 27834, 27861, 27897, 27906, 27942, 27946, 27982, 27987, 28005, 28015, 28041, 28045, 28067, 28095, 28178, 28185, 28186, 28221, 28238, 28249, 28282, 28315, 28338, 28374, 28379, 28441, 28522, 28527, 28538, 28543, 28554, 28671, 28698, 28707, 28726, 28734, 28742, 28762, 28806, 28819, 28835, 28851, 28878, 28885, 28945, 28954, 28966, 28977, 28986, 29002, 29013, 29014, 29015, 29045, 29049, 29103, 29121, 29166, 29193, 29203, 29206, 29218, 29222, 29246, 29279, 29281, 29323, 29418, 29481, 29563, 29589, 29607, 29643, 29665, 29679, 29697, 29706, 29742, 29746, 29805, 29815, 29859, 29922, 29949, 29967, 29971, 29998, 30002, 30003, 30073, 30138, 30149, 30194, 30205, 30219, 30255, 30266, 30277, 30291, 30302, 30355, 30363, 30506, 30535, 30561, 30583, 30622, 30642, 30651, 30687, 30709, 30742, 30793, 30795, 30831, 30838, 30874, 30889, 30957, 31002, 31027, 31074, 31093, 31126, 31137, 31154, 31182, 31186, 31191, 31195, 31217, 31227, 31245, 31254, 31263, 31274, 31283, 31297, 31331, 31335, 31353, 31426, 31533, 31551, 31569, 31622, 31623, 31655, 31659, 31686, 31717, 31787, 31858, 31894, 31929, 31947, 31983, 31993, 32019, 32055, 32082, 32091, 32145, 32181, 32215, 32249, 32253, 32271, 32302, 32379, 32383, 32414, 32426, 32433, 32442, 32469, 32478, 32485, 32486, 32514, 32523, 32542, 32586, 32591, 32594, 32622, 32631, 32635, 32642, 32685, 32695, 32721, 32734, 32757, 32774, 32793, 32794, 32795, 32818, 32874, 32878, 32929, 32973, 32998, 33031, 33062, 33063, 33089, 33115, 33153, 33155, 33243, 33245, 33254, 33263, 33269, 33333, 33355, 33383, 33387, 33423, 33439, 33441, 33459, 33497, 33542, 33553, 33567, 33578, 33598, 33603, 33611, 33634, 33655, 33657, 33722, 33738, 33745, 33747, 33801, 33818, 33839, 33846, 33865, 33882, 33909, 33927, 33981, 33985, 33995, 34098, 34105, 34134, 34142, 34151, 34161, 34181, 34206, 34222, 34226, 34262, 34323, 34354, 34357, 34377, 34435, 34458, 34466, 34494, 34523, 34538, 34539, 34558, 34611, 34701, 34719, 34726, 34746, 34751, 34765, 34773, 34809, 34865, 34867, 34882, 34926, 34962, 34979, 34989, 35034, 35042, 35045, 35115, 35155, 35165, 35169, 35186, 35187, 35203, 35205, 35214, 35241, 35306, 35313, 35326, 35405, 35483, 35538, 35542, 35546, 35565, 35583, 35637, 35705, 35777, 35785, 35835, 35845, 35861, 35889, 35979, 35989, 36023, 36046, 36051, 36087, 36142, 36159, 36177, 36214, 36222, 36249, 36258, 36274, 36281, 36302, 36314, 36337, 36346, 36438, 36445, 36449, 36474, 36515, 36526, 36533, 36537, 36546, 36555, 36565, 36573, 36593, 36627, 36646, 36699, 36746, 36757, 36766, 36803, 36835, 36874, 36879, 36898, 36907, 36917, 36933, 36958, 36994, 36998, 37005, 37058, 37066, 37095, 37111, 37113, 37162, 37167, 37205, 37221, 37222, 37293, 37302, 37315, 37329, 37373, 37414, 37454, 37482, 37545, 37562, 37563, 37595, 37626, 37689, 37723, 37743, 37761, 37789, 37797, 37806, 37843, 37869, 37887, 37927, 37934, 37973, 38006, 38066, 38085, 38193, 38211, 38218, 38233, 38274, 38283, 38301, 38319, 38337, 38369, 38382, 38395, 38399, 38471, 38482, 38485, 38517, 38526, 38542, 38545, 38554, 38562, 38591, 38695, 38706, 38735, 38787, 38818, 38845, 38855, 38886, 38893, 38895, 38902, 38905, 38909, 38931, 38947, 38967, 38969, 39022, 39046, 39055, 39074, 39093, 39121, 39122, 39174, 39201, 39219, 39255, 39274, 39282, 39355, 39399, 39426, 39482, 39579, 39597, 39658, 39705, 39759, 39802, 39845, 39849, 39867, 39878, 39885, 39903, 39923, 39957, 39991, 39995]

27521 is a cyclic, self and Duffinian number.

27521 can be rendered as a digital equation as follows:

2 + 7 = 5 * 2 - 1