27420 is a member of OEIS A062681: numbers that are sums of 2 or more consecutive squares in more than 1 way. Here two ways, viz. 55^2 + ... + 62^2 and 4^2 + ... + 43^2. The sequence can be generated as follows (permalink):

INPUT

target=27420

L=[]

for n in [1..100]:

  total=n^2

  S=[n]

  for i in [1..100]:

    total+=(n+i)^2

    S.append(n+i)

    if total<40000:

      L.append(total)

      if total==target:

        print(sorted(S))

        number=0

        for s in S:

          number+=s^2

        print("check confirms that sum of the terms squared is",target)

M=[]

for n in L:

  if L.count(n)>1:

    M.append(n)

print("The terms of the sequence are:")

print(sorted(Set(M)))

OUTPUT

[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43]

check confirms that sum of the terms squared is 27420

[55, 56, 57, 58, 59, 60, 61, 62]

check confirms that sum of the terms squared is 27420

The terms of the sequence are:

[365, 1405, 1730, 2030, 3281, 3655, 3740, 4510, 4705, 4760, 5244, 5434, 5915, 7230, 7574, 8415, 9385, 11055, 11900, 12325, 12524, 14905, 16745, 17484, 18879, 19005, 19855, 20449, 20510, 21790, 22806, 23681, 25580, 25585, 27230, 27420, 28985, 31395, 34224, 37114, 39606]

27420 is a Harshad, self, inconsummate and untouchable number. There are not many numbers that share these three properties. In fact, up to 40000, there are only 265 of them and they are:

872, 2672, 3752, 3818, 3842, 3864, 4046, 4316, 4338, 4382, 4472, 4494, 4742, 4832, 4854, 4898, 5126, 5148, 5372, 6654, 7284, 7598, 8162, 9152, 9218, 9264, 9848, 10076, 10368, 10379, 10412, 10884, 10974, 11481, 11516, 11549, 12594, 12752, 13226, 13259, 13314, 13382, 13742, 13922, 14126, 14148, 14328, 14394, 14418, 14664, 14754, 14798, 14822, 14934, 14978, 15116, 15215, 15452, 15474, 15507, 15597, 16251, 16811, 17217, 17285, 17544, 17588, 17621, 17757, 18141, 18387, 18422, 18837, 20325, 20514, 20874, 20918, 21392, 22316, 22652, 23214, 23664, 23888, 24722, 24755, 25071, 25104, 25317, 25374, 25418, 25464, 25532, 25622, 25655, 25868, 25901, 26039, 26981, 27029, 27420, 27444, 27611, 28142, 28254, 28377, 28388, 28511, 28737, 28748, 28926, 29165, 29187, 29222, 29244, 29321, 29424, 29435, 29760, 29995, 30337, 30348, 30359, 30449, 30651, 30774, 30998, 31057, 31147, 31237, 31292, 31314, 31428, 31439, 31584, 31707, 31764, 31808, 31832, 31922, 31955, 32025, 32036, 32047, 32069, 32091, 32137, 32159, 32214, 32394, 32418, 32429, 32484, 32552, 32574, 32585, 32618, 32732, 32798, 32822, 32855, 32934, 33037, 33059, 33092, 33114, 33171, 33239, 33698, 33911, 34082, 34374, 34385, 34587, 34655, 34699, 34767, 34925, 34947, 35105, 35151, 35318, 35432, 35454, 35577, 35588, 35621, 35757, 35847, 35880, 35891, 35924, 35948, 35981, 36029, 36095, 36207, 36242, 36264, 36275, 36365, 36398, 36422, 36444, 36455, 36488, 36510, 36567, 36578, 36624, 36635, 36701, 36769, 36791, 36813, 36837, 36848, 36859, 36927, 36949, 36960, 36971, 36993, 37015, 37085, 37175, 37197, 37232, 37265, 37298, 37421, 37434, 37478, 37489, 37535, 37568, 37579, 37623, 37680, 37781, 37803, 37827, 37838, 37871, 37926, 37928, 38005, 38154, 38165, 38220, 38310, 38378, 38525, 38760, 38916, 38927, 39144, 39221, 39537, 39548, 39581, 39671, 39704, 39783, 39851, 39917

27430 is an abundant, Zumkeller and pseudoperfect number.

27420 can be expressed as a digit equation as follows:

-2 + 7 - 4 = 2 ^ 0

27420 stabilises in about 1120 generations to several sliders and an assortment of still life shapes and oscillators.