114 (number): Difference between revisions
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==In mathematics== |
==In mathematics== |
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*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 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. |
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*114 is the smallest positive integer* which has yet to be represented as a³ + b³ + c³, [[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)³ + 80435758145817515³ + 12602123297335631³?”|last=Houston|first=Robin|date=2019-09-06|website=The Aperiodical|language=en|url-status=live|archive-url=|archive-date=|access-date=2019-12-28}}</ref> |
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*There is no answer to the equation [[Euler's totient function|φ]](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 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> |
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*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 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). |
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Revision as of 09:15, 28 December 2019
 | This article needs additional citations for verification. (May 2014) |
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|---|---|---|---|---|
| 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 | |||
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 other fields
- One hundred [and] fourteen is also
- Cadmium-114m is a radioisotope and nuclear isomer with a halflife of 14.1 years
- The atomic number of flerovium
- G.114 is an 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 Surah (Chapters) in the Quran (Holy book of Islam)
- The number of logion in the Gospel of Thomas
- The maximum number of points a team can obtain in one season in the Premier League.
See also
References
- ^ "Sloane's A007304 : Sphenic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
- ^ "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
- ^ Houston, Robin (2019-09-06). "42 is the answer to the question "what is (-80538738812075974)³ + 80435758145817515³ + 12602123297335631³?"". The Aperiodical. Retrieved 2019-12-28.
{{cite web}}: CS1 maint: url-status (link) - ^ "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
- ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.