6

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6 < 5 | 7 >
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

Visualization of 6

• 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, 10⁶ is the boundary between class 1 and class 2 numbers, 10¹⁰⁶ 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. This started a joke in the Japanese googology community that 6 was a large number.
• 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

• Busy Beaver Function: \(\Sigma(3)=6\)
• Maximum shifts function: \(S(2)=6\)
• Subcubic graph number: \(\text{SCG}(0)=6\)
• Xi function: \(\Xi(5) = 6\)