27638 is a sphenic number whose three distinct prime factors have no digital root in common and whose digital root is different from the digital root of the original number. The sequence can be generated as follows (permalink):
INPUT
L=[]
for n in [27638 .. 40000]:
if len(prime_factors(n))==3 and len(divisors(n))==8:
P=prime_factors(n)
R=[]
b=10
if sum(n.digits(b))%(b-1)!=0:
root=sum(n.digits())%(b-1)
else:
root=9
R.append(root)
for i in [0..2]:
b=10
if sum(P[i].digits(b))%(b-1)!=0:
root=sum(P[i].digits())%(b-1)
else:
root=9
R.append(root)
if len(R)==len(Set(R)):
a=len(list(P[0].digits()))+len(P[1].digits())+len(P[2].digits())
b=len(Set(P[0].digits()))+len(Set(P[1].digits()))+len(Set(P[2].digits()))
if a==b:
L.append(n)
OUTPUT
[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]
27638 is a Harshad number since it is a multiple of its sum of digits (26), and also a Moran number because the ratio is a prime number: 1063 = 27638 / (2 + 7 + 6 + 3 + 8).
27638 is an untouchable number because it is not equal to the sum of proper divisors of any number.
27638 is a nialpdrome in base 13 : c770
27638 is a super-3 number ince 3×27638^3 = 63334608774216, which contains 333 as substring.
27638 can be rendered as a digit equation as follows:
2 | (7 + 6 + 3) = 8
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