27362 is a product of 2 and a 4k+1 prime and so it can be expressed as a sum of two squares in one way only viz. 131^2 + 101^2.

27362 is a number n without the digit 0 with two distinct prime factors such that n + SOD(n) and n + POD(n) both have two distinct prime factors. Here SOD stands for sum of digits and POD for product of digits. Note that this is different to the arithmetic and multiplicative digital roots of a number. Here the results are 27382 = 2 * 13691 and 27866 = 2 * 13933 respectively.

The sequence can be generated as follows:

INPUT

S=[n for n in [1..40000] if len(prime_factors(n))==2 and len(divisors(n))==4]

L=[]

for n in S:

  D=n.digits()

  if 0 not in D:

    number1=n+sum(D)

    number2=n+prod(D)

    if (len(prime_factors(number1))==2 and len(divisors(number1))==4) and (len(prime_factors(number2))==2 and len(divisors(number2))==4): 

      L.append(n)

print(L)

print(len(L))

OUTPUT

[22, 26, 123, 134, 213, 291, 321, 411, 497, 566, 589, 671, 746, 763, 766, 789, 835, 862, 866, 889, 895, 921, 985, 1133, 1154, 1186, 1243, 1261, 1262, 1271, 1273, 1343, 1349, 1391, 1411, 1538, 1561, 1574, 1622, 1631, 1633, 1718, 1819, 1874, 1921, 1937, 1939, 1969, 2173, 2217, 2291, 2419, 2429, 2446, 2461, 2479, 2491, 2495, 2537, 2567, 2743, 2811, 2942, 2965, 2983, 3118, 3151, 3247, 3379, 3427, 3489, 3611, 3622, 3629, 3646, 3647, 3839, 3849, 3953, 3983, 4115, 4151, 4169, 4181, 4187, 4213, 4414, 4426, 4478, 4613, 4677, 4735, 4741, 4762, 4834, 4835, 4837, 4839, 4849, 4857, 4915, 4934, 4963, 5165, 5249, 5311, 5314, 5326, 5366, 5378, 5465, 5533, 5677, 5713, 5714, 5789, 5969, 5977, 6166, 6169, 6187, 6259, 6415, 6431, 6437, 6493, 6542, 6583, 6587, 6589, 6626, 6658, 6746, 6757, 6769, 6782, 6817, 6819, 6839, 7117, 7147, 7166, 7418, 7427, 7435, 7445, 7463, 7619, 7642, 7729, 7778, 7814, 7827, 7957, 7981, 7999, 8121, 8159, 8213, 8251, 8257, 8261, 8434, 8459, 8462, 8479, 8489, 8499, 8519, 8529, 8617, 8639, 8749, 8765, 8873, 8927, 8986, 9169, 9194, 9298, 9383, 9571, 9574, 9627, 9722, 9778, 9838, 9841, 9866, 9914, 9961, 9974, 11129, 11167, 11219, 11293, 11345, 11459, 11461, 11521, 11541, 11626, 11641, 11721, 11729, 11738, 11741, 11749, 11769, 11854, 11857, 12131, 12137, 12191, 12193, 12223, 12311, 12353, 12439, 12449, 12526, 12538, 12581, 12598, 12655, 12695, 12715, 12731, 12734, 12759, 12773, 12827, 12847, 12867, 12869, 12877, 13123, 13126, 13213, 13295, 13322, 13511, 13522, 13549, 13562, 13637, 13646, 13663, 13745, 13765, 13787, 13817, 13934, 13942, 13957, 13982, 13987, 14171, 14269, 14354, 14359, 14422, 14438, 14597, 14642, 14677, 14681, 14799, 14893, 14914, 14918, 14959, 14979, 14995, 15133, 15143, 15163, 15166, 15231, 15297, 15389, 15431, 15659, 15677, 15746, 15815, 15819, 15871, 15926, 15929, 15969, 15983, 16145, 16157, 16162, 16243, 16311, 16313, 16321, 16342, 16351, 16397, 16439, 16441, 16442, 16483, 16517, 16526, 16557, 16571, 16574, 16591, 16615, 16669, 16689, 16697, 16711, 16721, 16733, 16751, 16757, 16771, 16777, 16894, 16973, 17162, 17453, 17529, 17547, 17585, 17621, 17638, 17651, 17671, 17677, 17695, 17723, 17833, 17873, 17926, 18118, 18263, 18317, 18337, 18339, 18359, 18399, 18419, 18455, 18463, 18482, 18511, 18514, 18554, 18563, 18595, 18817, 18851, 18863, 18893, 18931, 19127, 19147, 19189, 19226, 19277, 19279, 19419, 19493, 19563, 19567, 19582, 19589, 19619, 19634, 19643, 19651, 19729, 19781, 19783, 19811, 19823, 19897, 19898, 19969, 21151, 21241, 21251, 21259, 21353, 21458, 21533, 21598, 21695, 21919, 21949, 21979, 22163, 22187, 22213, 22411, 22471, 22489, 22587, 22749, 22766, 22813, 22891, 22957, 22978, 22987, 23191, 23221, 23231, 23341, 23351, 23362, 23398, 23429, 23461, 23489, 23591, 23713, 23717, 23737, 23771, 23783, 23939, 23974, 23999, 24131, 24194, 24253, 24271, 24279, 24313, 24341, 24383, 24397, 24433, 24461, 24482, 24491, 24526, 24581, 24587, 24589, 24613, 24641, 24721, 24839, 24899, 25138, 25157, 25211, 25213, 25269, 25274, 25369, 25399, 25421, 25429, 25483, 25539, 25573, 25719, 25739, 25769, 25797, 25846, 25877, 25957, 25958, 26147, 26185, 26291, 26329, 26354, 26366, 26369, 26383, 26419, 26453, 26471, 26617, 26639, 26747, 26771, 26831, 26929, 26941, 26963, 27119, 27121, 27139, 27151, 27163, 27193, 27199, 27226, 27227, 27289, 27358, 27359, 27362, 27373, 27389, 27395, 27419, 27443, 27493, 27515, 27535, 27571, 27578, 27598, 27635, 27641, 27649, 27757, 27842, 27849, 27899, 27933, 27934, 28141, 28187, 28235, 28293, 28321, 28345, 28369, 28498, 28529, 28769, 28783, 28811, 28846, 28874, 28963, 29219, 29227, 29263, 29278, 29291, 29335, 29377, 29485, 29487, 29534, 29543, 29553, 29593, 29594, 29617, 29626, 29657, 29765, 29773, 29797, 29951, 31187, 31273, 31435, 31439, 31462, 31618, 31619, 31631, 31677, 31693, 31754, 31762, 31767, 31783, 31826, 31874, 31893, 32161, 32177, 32179, 32221, 32449, 32521, 32527, 32534, 32551, 32629, 32666, 32735, 32755, 32819, 32827, 32845, 32863, 32881, 33121, 33133, 33431, 33458, 33499, 33523, 33526, 33643, 33658, 33659, 33671, 33729, 33837, 33842, 33877, 33926, 33947, 33963, 33983, 34315, 34321, 34363, 34467, 34514, 34531, 34555, 34634, 34733, 34754, 34829, 34837, 34873, 34966, 34973, 34993, 35138, 35218, 35219, 35233, 35318, 35366, 35414, 35477, 35522, 35611, 35614, 35633, 35657, 35678, 35693, 35726, 35761, 35782, 35789, 35813, 35857, 35887, 35927, 36111, 36154, 36169, 36178, 36193, 36227, 36289, 36398, 36447, 36463, 36485, 36535, 36577, 36641, 36733, 36759, 36853, 36893, 36961, 37165, 37239, 37381, 37486, 37586, 37615, 37678, 37787, 37837, 37865, 37943, 37981, 38137, 38179, 38243, 38245, 38297, 38359, 38422, 38429, 38463, 38473, 38489, 38515, 38549, 38615, 38758, 38771, 38837, 38849, 38854, 38914, 38926, 38957, 38978, 38983, 38999, 39127, 39145, 39257, 39413, 39453, 39481, 39637, 39661, 39723, 39747, 39811, 39871, 39917, 39941, 39959]

27362 is a d-powerful number

27362 is an inconsummate number.

27362 stabilises after about 50 generations to a traffic light (four blinkers), a block and a glider.