| ||||
|---|---|---|---|---|
| Cardinal | one hundred five | |||
| Ordinal | 105th (one hundred fifth) | |||
| Factorization | 3 × 5 × 7 | |||
| Divisors | 1, 3, 5, 7, 15, 21, 35, 105 | |||
| Greek numeral | ΡΕ´ | |||
| Roman numeral | CV | |||
| Binary | 11010012 | |||
| Ternary | 102203 | |||
| Senary | 2536 | |||
| Octal | 1518 | |||
| Duodecimal | 8912 | |||
| Hexadecimal | 6916 | |||
105 (one hundred [and] five) is the natural number following 104 and preceding 106.
In mathematics
[edit]105 is a triangular number, a dodecagonal number,[1] and the first Zeisel number.[2] It is the first odd sphenic number and is the product of three consecutive prime numbers. 105 is the double factorial of 7.[3] It is also the sum of the first five square pyramidal numbers.
105 comes in the middle of the prime quadruplet (101, 103, 107, 109). The only other such numbers less than a thousand are 9, 15, 195, and 825.
105 is also the middle of the only prime sextuplet (97, 101, 103, 107, 109, 113) between the ones occurring at 7-23 and at 16057–16073. 105 is the product of the first three odd primes () and is less than the square of the next prime (11) by > 8. Therefore, for , n ± 2, ± 4, and ± 8 must be prime (a prime k-tuple). In contrast, n ± 6, ± 10, ± 12, and ± 14 must be composite, making a prime gap on either side.
105 is also a pseudoprime to the prime bases 13, 29, 41, 43, 71, 83, and 97. The distinct prime factors of 105 add up to 15, and so do those of 104; hence, the two numbers form a Ruth-Aaron pair under the first definition.
105 is also a number n for which is prime, for . (This even works up to , ignoring the negative sign.)
105 is the smallest integer such that the factorization of over Q includes non-zero coefficients other than . In other words, the 105th cyclotomic polynomial, Φ105, is the first with coefficients other than .
105 is the number of parallelogram polyominoes with 7 cells.[4]
In science
[edit]- The atomic number of dubnium.
In other fields
[edit]105 is also:
- A Shimano Road groupset since 1984
See also
[edit]References
[edit]- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134
- ^ "Sloane's A051624 : 12-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ "Sloane's A051015 : Zeisel numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ "Sloane's A006882 : Double factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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