2016 (number)
From HandWiki
Short description: Hardy-Ramanujan number
Short description: Natural number
| ||||
|---|---|---|---|---|
| Cardinal | two thousand sixteen | |||
| Ordinal | 2016th (two thousand sixteenth) | |||
| Factorization | 25 × 32 × 7 | |||
| Divisors | 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016 | |||
| Greek numeral | ,ΒΙϚ´ | |||
| Roman numeral | MMXVI | |||
| Binary | 111111000002 | |||
| Ternary | 22022003 | |||
| Quaternary | 1332004 | |||
| Quinary | 310315 | |||
| Senary | 132006 | |||
| Octal | 37408 | |||
| Duodecimal | 120012 | |||
| Hexadecimal | 7E016 | |||
| Vigesimal | 50G20 | |||
| Base 36 | 1K036 | |||
2016 is the natural number following 2015 and preceding 2017.
In mathematics
- 2016 is a triangular number, being 1 + 2 + 3 + ... + 63. Equivalently, [math]\displaystyle{ \tbinom{64}{2} = 2016 }[/math].
- 2016 is a 24-gonal number (sequence A051876 in the OEIS) and a generalized 28-gonal (icosioctagonal) number (sequence A303812 in the OEIS).
- 2016 has 36 divisors.
- 211 − 25 = 2016.
- 2016 forms a friendly pair with 360, as [math]\displaystyle{ \dfrac{\sigma(360)}{360} = \dfrac{1170}{360} = \dfrac{13}{4} = 3.25 }[/math] and [math]\displaystyle{ \dfrac{\sigma(2016)}{2016} = \dfrac{6552}{2016} = \dfrac{13}{4} = 3.25 }[/math]. The number 360 itself is a highly composite number, while 2016, while not highly composite, is highly composite among the positive integers not divisible by five.
- 2016 × 2 + 1 = 4033. Although 4033 is not prime, as 4033 = 37 × 109, it is a strong pseudoprime to base 2 (sequence A001262 in the OEIS). Aside from 2016, the only other numbers below 10,000 with this property are 1023, 1638, 2340, 4160, and 7920.
- There are 2016 five-cubes in a nine-cube.
- 2016 is an Erdős–Nicolas number (sequence A194472 in the OEIS) because, while not perfect, 2016 is the sum of its first 31 divisors (up to and including 288).
- 2016 × 20 = 40,320 = [math]\displaystyle{ 8! }[/math] (read as "8 factorial").
- [math]\displaystyle{ {{2016^{17}+1}\over 2017} }[/math] is prime. Since 2017 is similarly prime, 201617 + 1 is a semiprime. (sequence A104494 in the OEIS)
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