27656 is a product of a power of 2 and a 4k+1 prime and so it can be expressed as a sum of two squares in one way only viz. 10^2+166^2.

27656 is a number whose totient (13824) can be expressed as a cubic number (24^3). The sequence can be generated as follows:

INPUT

L=[]

for n in [1..40000]:

  if (euler_phi(n))^(1/3)==int((euler_phi(n))^(1/3)):

    L.append(n)

print(L)

print(len(L))

OUTPUT

[1, 2, 15, 16, 20, 24, 30, 85, 128, 136, 160, 170, 192, 204, 240, 247, 259, 327, 333, 351, 399, 405, 436, 494, 518, 532, 648, 654, 666, 684, 702, 756, 771, 798, 810, 1024, 1028, 1088, 1111, 1255, 1280, 1360, 1375, 1536, 1542, 1632, 1843, 1853, 1875, 1920, 2008, 2040, 2165, 2222, 2261, 2405, 2500, 2510, 2555, 2619, 2750, 2847, 2907, 3012, 3213, 3285, 3464, 3488, 3686, 3705, 3706, 3750, 3796, 3848, 3885, 3952, 4088, 4095, 4119, 4144, 4256, 4330, 4360, 4369, 4522, 4810, 4940, 5110, 5180, 5184, 5196, 5232, 5238, 5256, 5320, 5328, 5472, 5492, 5508, 5616, 5694, 5772, 5814, 5928, 6031, 6048, 6132, 6216, 6331, 6384, 6426, 6480, 6540, 6552, 6570, 6660, 6840, 7020, 7295, 7410, 7560, 7770, 7980, 8190, 8192, 8224, 8238, 8704, 8738, 8751, 8829, 8991, 9291, 9477, 10025, 10227, 10240, 10269, 10280, 10625, 10773, 10880, 10935, 11275, 11668, 11672, 12003, 12062, 12288, 12336, 12388, 12423, 12662, 12801, 13056, 13233, 13315, 13636, 14089, 14590, 14611, 14989, 15360, 15375, 15420, 16004, 16064, 16133, 16320, 16564, 16665, 17068, 17285, 17496, 17502, 17508, 17532, 17563, 17604, 17644, 17658, 17776, 17945, 17982, 18335, 18468, 18582, 18954, 20000, 20050, 20080, 20195, 20200, 20412, 20454, 20500, 20538, 20763, 20817, 20995, 21243, 21250, 21304, 21423, 21546, 21870, 22000, 22015, 22083, 22220, 22261, 22503, 22550, 22581, 23341, 24006, 24096, 24213, 24531, 24846, 25602, 25965, 26055, 26061, 26466, 26481, 26630, 26664, 27331, 27359, 27371, 27645, 27656, 27712, 27787, 27795, 27904, 28178, 28305, 28324, 28564, 28565, 28712, 29222, 29263, 29336, 29444, 29488, 29648, 29835, 29978, 30000, 30004, 30120, 30300, 30368, 30555, 30750, 30784, 31559, 31616, 31956, 32266, 32284, 32312, 32704, 32708, 32767, 33000, 33152, 33330, 33383, 33592, 33875, 33915, 34048, 34570, 34640, 34748, 34880, 35126, 35224, 35308, 35890, 36176, 36670, 36860, 37060, 37960, 38480, 39520]

291

27656 is a number that requires 38 steps to reach the palindrome 6839849878998789489386 under the Reverse and Add algorithm.

27656 is a tau number because it is divible by the number of its divisors (8).

27656 can be rendered as a digit equation as follows:

-2 + 7 = 6 + 5 - 6