363 (number) explained

Number:	363
Divisor:	1, 3, 11, 33, 121, 363

363 (three hundred [and] sixty-three) is the natural number following 362 and preceding 364.

In mathematics

• It is an odd, composite, positive, real integer, composed of a prime (3) and a prime squared (11²).
• 363 is a deficient number and a perfect totient number.
• 363 is a palindromic number in bases 3, 10, 11 and 32.
• 363 is a repdigit (BB) in base 32.
• The Mertens function returns 0.^[1]
• Any subset of its digits is divisible by three.
• 363 is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).
• 363 is the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243).
• 363 can be expressed as the sum of three squares in four different ways: 11² + 11² + 11², 5² + 7² + 17², 1² + 1² + 19², and 13² + 13² + 5².
• 363 cubits is the solution given to Rhind Mathematical Papyrus question 50 – find the side length of an octagon with the same area as a circle 9 khet in diameter http://www.seshat.ch/home/rhind6.htm.

Notes and References

1. Web site: Sloane's A028442 : Numbers n such that Mertens' function is zero. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-02.