114 (number): Difference between revisions

← 113 114 115 →
← 110 111 112 113 114 115 116 117 118 119 → List of numbers; Integers; ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred fourteen
Ordinal	114th; (one hundred fourteenth)
Factorization	2 × 3 × 19
Divisors	1, 2, 3, 6, 19, 38, 57, 114
Greek numeral	ΡΙΔ´
Roman numeral	CXIV
Binary	11100102
Ternary	110203
Senary	3106
Octal	1628
Duodecimal	9612
Hexadecimal	7216

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114 (one hundred [and] fourteen) is the natural number following 113 and preceding 115.

In mathematics

114 is an abundant number, a sphenic number^[1] and a Harshad number.^[2] It is the sum of the first four hyperfactorials, including H(0). At 114, the Mertens function sets a new low of -6, a record that stands until 197.
114 is the smallest positive integer* which has yet to be represented as a³ + b³ + c³, where a, b, and c are integers. It is conjectured that 114 can be represented this way. (*Excluding integers of the form 9k ± 4, for which solutions are known not to exist.)^[3]
There is no answer to the equation φ(x) = 114, making 114 a nontotient.^[4]
114 appears in the Padovan sequence,^[5] preceded by the terms 49, 65, 86 (it is the sum of the first two of these).
114 is a repdigit in base 7 (222).

In religion

There are 114 chapters, or surahs, in the Quran.

There are 114 sayings in The Gospel of Thomas.

References

^ Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers: products of 3 distinct primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Houston, Robin (2019-09-06). "42 is the answer to the question "what is (-80538738812075974)³ + 80435758145817515³ + 12602123297335631³?"". The Aperiodical. Retrieved 2019-12-28.
^ Sloane, N. J. A. (ed.). "Sequence A005277 (Nontotients: even numbers k such that phi(m) = k has no solution)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 0)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[1] Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers: products of 3 distinct primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[2] Sloane, N. J. A. (ed.). "Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[3] Houston, Robin (2019-09-06). "42 is the answer to the question "what is (-80538738812075974)³ + 80435758145817515³ + 12602123297335631³?"". The Aperiodical. Retrieved 2019-12-28.

[4] Sloane, N. J. A. (ed.). "Sequence A005277 (Nontotients: even numbers k such that phi(m) = k has no solution)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[5] Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 0)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

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@@ Line 1: / Line 1: @@
-{{Refimprove|date=May 2014}}
 {{Infobox number
-| numb 58
+| number = 114
 | divisor = 1, 2, 3, 6, 19, 38, 57, 114
 }}
@@ Line 7: / Line 6: @@
 ==In mathematics==
-*114 is an [[abundant number]], a [[sphenic number]]<ref>{{Cite web|url=https://oeis.org/A007304|title=Sloane's A007304 : Sphenic numbers|last=|first=|date=|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-26}}</ref> and a [[Harshad number]].<ref>{{Cite web|url=https://oeis.org/A005349|title=Sloane's A005349 : Niven (or Harshad) numbers|last=|first=|date=|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-26}}</ref> It is the sum of the first four [[hyperfactorial]]s, including H(0). At 114, the [[Mertens function]] sets a new low of -6, a record that stands until 197.
+*114 is an [[abundant number]], a [[sphenic number]]<ref>{{Cite OEIS|A007304|Sphenic numbers: products of 3 distinct primes}}</ref> and a [[Harshad number]].<ref>{{Cite OEIS|A005349|Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits}}</ref> It is the sum of the first four [[hyperfactorial]]s, including H(0). At 114, the [[Mertens function]] sets a new low of -6, a record that stands until 197.
+*114 is the smallest positive integer* which has yet to be represented as a<sup>3</sup> + b<sup>3</sup> + c<sup>3</sup>, [[Sums of three cubes|where a, b, and c are integers]]. It is conjectured that 114 can be represented this way. (*Excluding integers of the form 9k ± 4, for which solutions are known not to exist.)<ref>{{Cite web|url=https://aperiodical.com/2019/09/42-is-the-answer-to-the-question-what-is-80538738812075974%c2%b3-80435758145817515%c2%b3-12602123297335631%c2%b3/|title=42 is the answer to the question "what is (-80538738812075974)<sup>3</sup> + 80435758145817515<sup>3</sup> + 12602123297335631<sup>3</sup>?"|last=Houston|first=Robin|date=2019-09-06|website=The Aperiodical|language=en|access-date=2019-12-28}}</ref>
-*There is no answer to the equation [[Euler's totient function|&phi;]](x) = 114, making 114 a [[nontotient]].<ref>{{Cite web|url=https://oeis.org/A005277|title=Sloane's A005277 : Nontotients|last=|first=|date=|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-26}}</ref>
+*There is no answer to the equation [[Euler's totient function|φ]](x) = 114, making 114 a [[nontotient]].<ref>{{Cite OEIS|A005277|2=Nontotients: even numbers k such that phi(m) = k has no solution}}</ref>
-*114 appears in the [[Padovan sequence]],<ref>{{Cite web|url=https://oeis.org/A000931|title=Sloane's A000931 : Padovan sequence|last=|first=|date=|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-26}}</ref> preceded by the terms 49, 65, 86 (it is the sum of the first two of these).
+*114 appears in the [[Padovan sequence]],<ref>{{Cite OEIS|A000931|2=Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 0}}</ref> preceded by the terms 49, 65, 86 (it is the sum of the first two of these).
 *114 is a [[repdigit]] in base 7 (222).
-==In other fields==
+==In religion==
-;One hundred [and] fourteen is also:
+There are 114 chapters, or surahs, in the [[Quran]].
-* [[Cadmium]]-114m is a [[radioisotope]] and [[nuclear isomer]] with a [[halflife]] of 14.1 years
-* The [[atomic number]] of [[flerovium]]
+There are 114 sayings in [[The Gospel of Thomas]].
-* [[G.114]] is an [[International Telecommunication Union|ITU]] recommendation for acceptable delays for voice application in telecommunications
-* The [[police]] non-emergency number in [[Denmark]] and [[Germany]]
-* The [[fire]] [[emergency telephone]] number in [[Vietnam]]
-* The medical emergency/ambulance number in [[Mauritius]]
-* The online and [[telephone directory]] number in [[Israel]].
-* The number of Surahs (Chapters) in the Quran (Holy book of Islam)
-* The maximum number of points a team can obtain in one season in the [[Premier League]].
 ==See also==
-* [[114]] (year)
+* [[114 (disambiguation)]]
-* [[List of highways numbered 114]]
-* [[CRM 114 (device)]]
-* [[CRM114 (program)]]
 ==References==
@@ Line 37: / Line 28: @@
 {{DEFAULTSORT:114 (Number)}}
 [[Category:Integers]]
-[[Category:Communications in Mauritius]]