6 - Revision history

Vipul: /* Properties and families */

2012-07-03T18:00:55Z

Properties and families

← Older revision		Revision as of 18:00, 3 July 2012
Line 14:		Line 14:
	! Property or family !! Parameter values !! First few members of the family !! Proof of satisfaction/membership/containment		! Property or family !! Parameter values !! First few members of the family !! Proof of satisfaction/membership/containment
	\|-		\|-
	\| [[perfect number]]: number <math>n</math> such that the divisor sum function of <math>n</math> is <math>2n</math> \|\| first perfect number \|\| {{#lst:perfect number\|list}} \|\| divisor sum is <math>1 + 2 + 3 + 6 = 12 = 2(6)</math>		\| [[satisfies property::perfect number]]: number <math>n</math> such that the divisor sum function of <math>n</math> is <math>2n</math> \|\| first perfect number \|\| {{#lst:perfect number\|list}} \|\| divisor sum is <math>1 + 2 + 3 + 6 = 12 = 2(6)</math>
	\|-		\|-
	\| [[primorial]]: product of the first few prime numbers \|\| product of the first two prime numbers (if we start the indexing from the zeroth primorial, which is an empty product and evaluates to 1, it is the ''third'' in the list) \|\| {{#lst:primorial\|list}} \|\| The first two primes are 2 and 3, and their product is 6.		\| [[satisfies property::primorial]]: product of the first few prime numbers \|\| product of the first two prime numbers (if we start the indexing from the zeroth primorial, which is an empty product and evaluates to 1, it is the ''third'' in the list) \|\| {{#lst:primorial\|list}} \|\| The first two primes are 2 and 3, and their product is 6.
	\|-		\|-
	\| [[factorial]]: product of the first few natural numbers \|\| product of the first three natural numbers (if we start the indexing from the zeroth factorial, which is an empty product and evaluates to 1, it is the ''fourth'' in the list) \|\| {{#lst:factorial\|list}} \|\| <math>1 \cdot 2 \cdot 3 = 6</math>		\| [[satisfies property::factorial]]: product of the first few natural numbers \|\| product of the first three natural numbers (if we start the indexing from the zeroth factorial, which is an empty product and evaluates to 1, it is the ''fourth'' in the list) \|\| {{#lst:factorial\|list}} \|\| <math>1 \cdot 2 \cdot 3 = 6</math>
	\|-		\|-
	\| [[lcm of all numbers so far]]: lcm of the first few natural numbers \|\| lcm of the first three natural numbers \|\| {{#lst:lcm of all numbers so far\|list}} \|\| <math>\operatorname{lcm} \{ 1,2,3 \} = 6</math>.		\| [[satisfies property::lcm of all numbers so far]]: lcm of the first few natural numbers \|\| lcm of the first three natural numbers \|\| {{#lst:lcm of all numbers so far\|list}} \|\| <math>\operatorname{lcm} \{ 1,2,3 \} = 6</math>.
	\|}		\|}

Vipul: /* Properties and families */

2012-07-03T17:54:05Z

Properties and families

← Older revision		Revision as of 17:54, 3 July 2012
Line 19:		Line 19:
	\|-		\|-
	\| [[factorial]]: product of the first few natural numbers \|\| product of the first three natural numbers (if we start the indexing from the zeroth factorial, which is an empty product and evaluates to 1, it is the ''fourth'' in the list) \|\| {{#lst:factorial\|list}} \|\| <math>1 \cdot 2 \cdot 3 = 6</math>		\| [[factorial]]: product of the first few natural numbers \|\| product of the first three natural numbers (if we start the indexing from the zeroth factorial, which is an empty product and evaluates to 1, it is the ''fourth'' in the list) \|\| {{#lst:factorial\|list}} \|\| <math>1 \cdot 2 \cdot 3 = 6</math>
			\|-
			\| [[lcm of all numbers so far]]: lcm of the first few natural numbers \|\| lcm of the first three natural numbers \|\| {{#lst:lcm of all numbers so far\|list}} \|\| <math>\operatorname{lcm} \{ 1,2,3 \} = 6</math>.
	\|}		\|}

Vipul at 17:32, 3 July 2012

2012-07-03T17:32:58Z

@@ Line 19: / Line 19: @@
 |-
 | [[factorial]]: product of the first few natural numbers || product of the first three natural numbers (if we start the indexing from the zeroth factorial, which is an empty product and evaluates to 1, it is the ''fourth'' in the list) || {{#lst:factorial|list}} || <math>1 \cdot 2 \cdot 3 = 6</math>
 |}

Vipul: Created page with "{{particular natural number}} ==Summary== ===Factorization=== The number 6 has the following factorization, with prime factors 2 and 3: $6 = 2^1 \cdot 3^1 = 2..."$

2012-07-03T17:31:24Z

Created page with "{{particular natural number}} ==Summary== ===Factorization=== The number 6 has the following factorization, with prime factors 2 and 3: <math>6 = 2^1 \cdot 3^1 = 2..."

New page

{{particular natural number}}

==Summary==

===Factorization===

The number 6 has the following factorization, with prime factors [[2]] and [[3]]:

<math>6 = 2^1 \cdot 3^1 = 2 \cdot 3</math>

===Properties and families===

{| class="sortable" border="1"
! Property or family !! Parameter values !! First few members of the family !! Proof of satisfaction/membership/containment
|-
| [[perfect number]]: number <math>n</math> such that the divisor sum function of <math>n</math> is <math>2n</math> || first perfect number || {{#lst:perfect number|list}} || divisor sum is <math>1 + 2 + 3 + 6 = 12 = 2(6)</math>
|-
| [[primorial]]: product of the first few prime numbers || product of the first two prime numbers (if we start the indexing from the zeroth primorial, which is an empty product and evaluates to 1, it is the ''third'' in the list) || {{#lst:primorial|list}} || The first two primes are 2 and 3, and their product is 6.
|-
| [[factorial]]: product of the first few natural numbers || product of the first three natural numbers (if we start the indexing from the zeroth factorial, which is an empty product and evaluates to 1, it is the ''fourth'' in the list) || {{#lst:factorial|list}} || <math>1 \cdot 2 \cdot 3 = 6</math>
|}

6 - Revision history

Vipul: /* Properties and families */

Vipul: /* Properties and families */

Vipul at 17:32, 3 July 2012

Vipul: Created page with "{{particular natural number}} ==Summary== ===Factorization=== The number 6 has the following factorization, with prime factors 2 and 3: 6 = 2^1 \cdot 3^1 = 2..."

Vipul: Created page with "{{particular natural number}} ==Summary== ===Factorization=== The number 6 has the following factorization, with prime factors 2 and 3: $6 = 2^1 \cdot 3^1 = 2..."$