6 | |||||||||
---|---|---|---|---|---|---|---|---|---|

Numbers 0 - 99 | |||||||||

0 | 1 | 2 | 3 | 4 | 5 | 6 |
7 | 8 | 9 |

10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |

20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |

30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |

40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |

50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 |

60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 |

70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 |

80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 |

90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 |

**6 (six)** is a positive integer following 5 and preceding 7. Its ordinal form is written "sixth" or "6th".

## Properties

6 is an even number, the third triangular number, the third factorial number, and 3 or 4 primorial.

- 6 is equal to the sum of its proper divisors: 1 + 2 + 3 = 6. This makes it a perfect number, and in fact the smallest number with that property, with the next being 28.
- 6 is equal to the sum of its unitary proper divisors, that is to say divisors d such that d and n/d are relatively prime. These are called unitary perfect numbers. It is the smallest number with this property.
- It is the only semiprime number to not also be a deficient number.
- It is the smallest number N such that all multiples of N are abundant. All perfect or abundant numbers have this property.
- In the Czech language, 6 is called "půltucet", meaning "half-twelve".

## In googology

- Some googologisms based on 6 are sextoogol, superhex and the hexalogue. It is not commonly found in googology.
- Six is the basis of Robert Munafo's idea of classes. 6 is the boundary between class 0 and class 1 numbers, 10
^{6}is the boundary between class 1 and class 2 numbers, 10^{106}is the boundary between class 2 and class 3 numbers, and so on. - The Misalian seximal system uses base six, which is also called senary or heximal.
- In Greek-based number naming systems, 6 is associated with prefix hexa-, and with prefix sexti- in Latin systems.
- 6 is the last digit of mega.
- Flan number 4 version 2 (or フラン数第四形態改二 in Japanese) is equal to 6.
- ６ (or 全角の6 in Japanese) is a specific value of a function in a version N3.0 of N primitive. The shape of the letter looks quite similar to 6, but the value is shown to be greater than 6.

### Googological functions returning 6

- Rado's Sigma Function: \(\Sigma(3)=6\)
- Maximum shifts function: \(S(2)=6\)
- Subcubic graph number: \(\text{SCG}(0)=6\)
- Xi function: \(\Xi(5) = 6\)

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