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 |
*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. |
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*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> |
*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> |
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*There is no answer to the equation [[Euler's totient function|φ]](x) = 114, making 114 a [[nontotient]].<ref>{{Cite |
*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> |
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*114 appears in the [[Padovan sequence]],<ref>{{Cite |
*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). |
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*114 is a [[repdigit]] in base 7 (222). |
*114 is a [[repdigit]] in base 7 (222). |
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==References== |
==References== |
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{{reflist}} |
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{{Integers|1}} |
{{Integers|1}} |
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Revision as of 14:00, 21 May 2024
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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 religion
There are 114 chapters, or surahs, in the Quran.
There are 114 sayings in The Gospel of Thomas.
See also
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.