In Mathematics
85 is an octahedral number, a centered triangular number, a centered square number, a decagonal number, and a Smith number.
85 is the product of two prime numbers (5 and 17), and is therefore a biprime; specifically, the 24th biprime not counting perfect squares. Together with 86 and 87, it forms the second cluster of three consecutive biprimes.
85 can be expressed as a sum of two squares in two ways, 85= 92 + 22 = 72 + 62
85 is 1111 (a repunit) in base 4; which is expected, since its two factors 5 and 17 are consecutive Fermat primes, and the base 4 is one less than the smaller factor 5.
The aliquot sum of 85 is 23 within the aliquot sequence (23,1,0) 85 being the second composite number in the 23-aliquot tree.
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