1729 - Revision history

Vipul: /* Properties and families */

2024-07-14T20:18:04Z

Properties and families

← Older revision		Revision as of 20:18, 14 July 2024
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	! Property or family !! Parameter values !! First few members !! Proof of membership/containment/satisfaction		! Property or family !! Parameter values !! First few members !! Proof of membership/containment/satisfaction
	\|-		\|-
	\| [[Carmichael number]] \|\| third among them \|\| {{#lst:Carmichael number\|list}} \|\| The universal exponent is <math>\operatorname{lcm}\{ 6, 12, 18\} = 36</math> which divides 1728.		\| [[satsfies property::Carmichael number]] \|\| third among them \|\| {{#lst:Carmichael number\|list}} \|\| The universal exponent is <math>\operatorname{lcm}\{ 6, 12, 18\} = 36</math> which divides 1728.
	\|-		\|-
	\| [[Poulet number]] ([[Fermat pseudoprime]] to base 2) \|\| sixth among them \|\| {{#lst:Poulet number\|list}} \|\| follows from being a Carmichael number.		\| [[satisfies property::Poulet number]] ([[Fermat pseudoprime]] to base 2) \|\| sixth among them \|\| {{#lst:Poulet number\|list}} \|\| follows from being a Carmichael number.
	\|}		\|}

Vipul: /* Properties and families */

2012-01-15T21:21:52Z

Properties and families

← Older revision		Revision as of 21:21, 15 January 2012
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Property or family !! Parameter values !! First few ~~numbers~~		! Property or family !! Parameter values !! First few members !! Proof of membership/containment/satisfaction
	\|-		\|-
	\| [[Carmichael number]] \|\| third among them \|\| ~~[[561]]~~, ~~[[1105]]~~, ~~[[1729]], ..~~.		\| [[Carmichael number]] \|\| third among them \|\| {{#lst:Carmichael number\|list}} \|\| The universal exponent is <math>\operatorname{lcm}\{ 6, 12, 18\} = 36</math> which divides 1728.
	\|-		\|-
	\| [[Poulet number]] ([[Fermat pseudoprime]] to base 2) \|\| sixth among them \|\| ~~[[341]], [[561]], [[645]], [[1105]], [[1387]], [[1729]], [[1905]], [[2047]]~~		\| [[Poulet number]] ([[Fermat pseudoprime]] to base 2) \|\| sixth among them \|\| {{#lst:Poulet number\|list}} \|\| follows from being a Carmichael number.
	\|}		\|}

Vipul: /* Arithmetic functions */

2012-01-02T20:39:51Z

Arithmetic functions

← Older revision		Revision as of 20:39, 2 January 2012
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Function !! Value ~~!! Similar numbers~~ !! Explanation		! Function !! Value !! Explanation
	\|-		\|-
	\| {{arithmetic function value\|Euler totient function\|1296}} \|\| It is the product <math>(7 - 1)(13 - 1)(19 - 1) = (6)(12)(18) = 1296</math>.		\| {{arithmetic function value\|Euler totient function\|1296}} \|\| It is the product <math>(7 - 1)(13 - 1)(19 - 1) = (6)(12)(18) = 1296</math>.

Vipul: /* Properties and families */

2012-01-02T20:38:11Z

Properties and families

@@ Line 19: / Line 19: @@
 |-
 | [[Poulet number]] ([[Fermat pseudoprime]] to base 2) || sixth among them || [[341]], [[561]], [[645]], [[1105]], [[1387]], [[1729]], [[1905]], [[2047]]
 |}

Vipul: /* Names */

2012-01-02T20:30:19Z

Names

← Older revision		Revision as of 20:30, 2 January 2012
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	===Names===		===Names===

	This number is called the '''Hardy-Ramanujan number''' after a conversation between Hardy and Ramanujan where Ramanujan observed that it is the smallest number expressible as the sum of two cubes in two distinct ways: <math>\! 1729 = 10^3 + 9^23 = 12^3 + 1^3</math>.		This number is called the '''Hardy-Ramanujan number''' after a conversation between Hardy and Ramanujan where Ramanujan observed that it is the smallest number expressible as the sum of two cubes in two distinct ways: <math>\! 1729 = 10^3 + 9^3 = 12^3 + 1^3</math>.

	===Factorization===		===Factorization===

Vipul: /* Properties and families */

2012-01-02T20:29:59Z

Properties and families

← Older revision		Revision as of 20:29, 2 January 2012
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	\| [[Carmichael number]] \|\| third among them \|\| [[561]], [[1105]], [[1729]], ...		\| [[Carmichael number]] \|\| third among them \|\| [[561]], [[1105]], [[1729]], ...
	\|-		\|-
	\| [[Poulet number]] ([[Fermat pseudoprime to base 2) \|\| sixth among them \|\| [[341]], [[561]], [[645]], [[1105]], [[1387]], [[1729]], [[1905]], [[2047]]		\| [[Poulet number]] ([[Fermat pseudoprime]] to base 2) \|\| sixth among them \|\| [[341]], [[561]], [[645]], [[1105]], [[1387]], [[1729]], [[1905]], [[2047]]
	\|}		\|}

Vipul: Created page with "{{particular number}} ==Summary== ===Names=== This number is called the '''Hardy-Ramanujan number''' after a conversation between Hardy and Ramanujan where Ramanujan observ..."

2012-01-02T20:29:45Z

Created page with "{{particular number}} ==Summary== ===Names=== This number is called the '''Hardy-Ramanujan number''' after a conversation between Hardy and Ramanujan where Ramanujan observ..."

New page

{{particular number}}

==Summary==

===Names===

This number is called the '''Hardy-Ramanujan number''' after a conversation between Hardy and Ramanujan where Ramanujan observed that it is the smallest number expressible as the sum of two cubes in two distinct ways: <math>\! 1729 = 10^3 + 9^23 = 12^3 + 1^3</math>.

===Factorization===

<math>\! 1729 = 7 \cdot 13 \cdot 19</math>

===Properties and families===

{| class="sortable" border="1"
! Property or family !! Parameter values !! First few numbers
|-
| [[Carmichael number]] || third among them || [[561]], [[1105]], [[1729]], ...
|-
| [[Poulet number]] ([[Fermat pseudoprime to base 2) || sixth among them || [[341]], [[561]], [[645]], [[1105]], [[1387]], [[1729]], [[1905]], [[2047]]
|}