27365 is a sphenic number and product of primes that are the larger of twin prime pairs; sum of squares of number pairs. See blog post Triple Strength Sphenic Numbers And More. There are 166 such numbers in the range up to 40,000:

455, 665, 1085, 1235, 1505, 1729, 2015, 2135, 2555, 2795, 2821, 2945, 3605, 3815, 3913, 3965, 4085, 4123, 4745, 4865, 5285, 5551, 5719, 5795, 6335, 6643, 6665, 6695, 6755, 6935, 6965, 7085, 7657, 8015, 8113, 8435, 9035, 9331, 9373, 9455, 9485, 9709, 9785, 9815, 9905, 9919, 10355, 10621, 10955, 11315, 11765, 12215, 12545, 12649, 12935, 13115, 13205, 13237, 13699, 13741, 14345, 14497, 14735, 14885, 15067, 15155, 15665, 15695, 15841, 15965, 16205, 16471, 16895, 17195, 17329, 17563, 17615, 18031, 18109, 18305, 18335, 18361, 18395, 18487, 18905, 19985, 20083, 20345, 20839, 21035, 21545, 21665, 21755, 21931, 21973, 22145, 22265, 22351, 22505, 22685, 22895, 23135, 23405, 23435, 23653, 24073, 24583, 24661, 25327, 25441, 25669, 25745, 25753, 26467, 26885, 26923, 27365, 28055, 28145, 28385, 28483, 28805, 29015, 29419, 29735, 29885, 29915, 30065, 30095, 30163, 30457, 30845, 30905, 31003, 31171, 31415, 31759, 32053, 32465, 32767, 32809, 33155, 33245, 33995, 34099, 34333, 35495, 35735, 35929, 36043, 36155, 36785, 37115, 37205, 37297, 37355, 37595, 37639, 38255, 38311, 38915, 39065, 39277, 39403, 39785, 39995

27365 is the product of three 4k+1 primes and thus can be expressed as a sum of two squares in four different way viz. the sum of squares of the number pairs (38, 161), (49, 158), (97, 134) and (106, 127).

27365 is an Ulam number.

27365 is a d-powerful number because it can be written as 2^11 + 7^5 + 3^6 + 6^5 + 5 .

27365 is a Duffinian, self, inconsummate, congruent & amenable number.

27365 stabilises after about 310 generations to a complex mix of two gliders as well as blocks, beehives and blinkers.