1728 ( one thousand seven hundred twenty eight ) is a natural number located between the numbers 1727 and 1729 . The number 1728 is equal to the obsolete measure of account - mass (dotsand) , it is also equal to a dozen grosses .
| 1728 | |
|---|---|
| one thousand seven hundred twenty eight | |
| ← 1726 1727 1728 1729 1730 → | |
| Factorization | 2 6 3 3 |
| Roman notation | MDCCXXVIII |
| Binary | 11011000000 |
| Octal | 3300 |
| Hexadecimal | 6C0 |
In Math
- 1728 = 12 3 [1] , so in the duodecimal notation, this number is written as 1000 , also it is the number of cubic inches in cubic foot [2] .
- 1728 = 3 3 × 4 3
- 1728 = 2 3 × 6 3
- 1728 = 6 3 + 8 3 + 10 3
- 1728 = 24 2 + 24 2 + 24 2
- Also, two parts of 1728 17 and 28 can be represented as sums of the first prime numbers:
- 17 = 2 + 3 + 5 + 7
- 28 = 2 + 3 + 5 + 7 + 11
- The number 1728 can be represented as the product of the first composite numbers [3] :
- 1728 = 4 × 6 × 8 × 9
- The previous and next numbers with this property are 192 and 17 280, respectively.
- For n = 1728,
- has exactly one integer solution [4] .
- There are 1728 permutations of numbers from 1 to 8, in which any two adjacent numbers are coprime [5] .
- 1728 is the integer area of the inscribed quadrangle with integer sides and the radius of the circumscribed circle [6] .
- The number 1728 is the second member of a sequence of cubes starting with the number 8, in which the decimal notation of any element is the suffix of the decimal notation of the following element:
- 8 , 1728 , 15 851 081 728 , 476 841 757 827 289 415 851 081 728 , ... (sequence A050648 in OEIS )
- Twelfth 28-coal number.
- It is a coefficient necessary for calculating the invariant of an elliptic curve .
- The number 1728 is the length [7] of one of the first generations of the Kolakoski sequence [8] .
- The number of spanning trees of the graph equal to 1728 [9] .
- The number 1728 is the second (after 64 ) cube , which is the arithmetic average of two consecutive primes ( Eng. Interprime ) [10] :
- The sum of the first 1728 Fibonacci numbers is divided by 1728 [11] [12] .
- There are 1728 positive integers that cannot be represented as the sum of pairwise distinct 23-angular numbers [13] .
- 1728 - fifth non-recurring composerial ( )
This is the only composerial that is simultaneously a cube [14] .
The next unique composer is 10! / 10 # = 11! / 11 # = 17280 [15] [3] [16] .
Notes
- ↑ sequence A000578 in OEIS , sequence A001021 in OEIS , sequence A001597 in OEIS
- ↑ Wells, 1987 .
- ↑ 1 2 sequence A036691 in OEIS
- ↑ sequence A179145 in OEIS
- ↑ sequence A076220 in OEIS
- ↑ sequence A210250 in OEIS
- ↑ sequence A054352 in OEIS
- ↑ sequence A000002 in OEIS
- ↑ sequence A003690 in OEIS
- ↑ sequence A234240 in OEIS
- ↑ sequence A111035 in OEIS
- ↑ Request to Wolfram Alpha :
sum(Fibonacci[i], i=1..1728) mod 1728 - ↑ sequence A025524 in OEIS Number of positive integers that are not the sum of distinct n-th-order polygonal numbers
- ↑ Tanya Khovanova. Number Gossip: 1728 www.numbergossip.com. Date of treatment February 1, 2018.
- ↑ compositorials . www.numbersaplenty.com. Date of treatment February 1, 2018.
- ↑ Compositorial - OeisWiki . oeis.org. Date of treatment February 1, 2018.
Literature
- David Wells. 1728 // The Penguin Dictionary of Curious and Interesting Numbers . - 1 st ed. - Penguin Books , 1987. - P. 165. - 229 p. - ISBN 0-14-008029-5 .
- Tanya Khovanova. Number Gossip: 1728 www.numbergossip.com. Date of treatment February 1, 2018.