216 (number)

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← 215 216 217 →
Cardinaltwo hundred sixteen
Ordinal216th
(two hundred sixteenth)
Factorization23× 33
Divisors1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
Greek numeralΣΙϚ´
Roman numeralCCXVI
Binary110110002
Ternary220003
Quaternary31204
Quinary13315
Senary10006
Octal3308
Duodecimal16012
HexadecimalD816
VigesimalAG20
Base 366036

216 (two hundred [and] sixteen) is the natural number following 215 and preceding 217.

One interpretation of Plato's number

Since 216 = 33 + 43 + 53 = 63, it is the smallest cube that is also the sum of three cubes (Plato was among the first to notice this, and mentioned it in Book VIII of Republic). It is also the sum of a twin prime (107 + 109). But since there is no way to express it as the sum of the proper divisors of any other integer, it is an untouchable number. This multiplicative magic square

has magic constant 216.

It has been conjectured that each natural number not equal to 216 can be written in the form p + Tx, where p is 0 or a prime, and Tx = x(x+1)/2 is a triangular number.[1]

In base 10, it is a Harshad number.

There are 216 fixed hexominoes, the polyominoes made from 6 squares.

216 is a Friedman number.

216 is the smallest number n, for which n−3, n−2, n−1, n+1, n+2, n+3 are all semiprimes.[2]

In other fields[edit]

See also[edit]

References[edit]

  1. ^ Zhi-Wei Sun. "Zhi-Wei Sun's homepage".
  2. ^ Sloane, N. J. A. (ed.). "Sequence A202319 (Twin semiprime-triples)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.