Which is the most composite number?
There are an infinite number of highly composite numbers, and the first few are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, (OEIS A002182). The corresponding numbers of divisors are 1, 2, 3, 4, 6, 8, 9, 10, 12, 16, 18, 20, 24, 30, 32, (OEIS A002183).
What are 5 composite numbers examples?
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Why are superior highly composite numbers used as Radices?
The first few superior highly composite numbers have often been used as radices, due to their high divisibility for their size. For example: Binary (base 2)
How much rating did Hardy gave to Ramanujan?
But Hardy did give Ramanujan the highest score for pure talent as reported by Paul Erdös, one of the most influential mathematicians of the 20-th century: Rating mathematicians on a scale of 1 to 100 for pure talent, Hardy gave himself a score of 25, his colleague Littlewood a score of 30, the great German …
Is 30 highly composite?
A highly composite number is a positive integer with more divisors than any smaller positive integer has. The term was coined by Ramanujan (1915)….Examples.
| n | d(n) | Divisors of n |
|---|---|---|
| 720 | 30 | 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720 |
Is 15 prime or composite?
Is 15 a Composite Number? Yes, since 15 has more than two factors i.e. 1, 3, 5, 15. In other words, 15 is a composite number because 15 has more than 2 factors.
Who is the creator of the highly composite number?
Highly composite number. The term was coined by Ramanujan (1915). However, Jean-Pierre Kahane has suggested that the concept might have been known to Plato, who set 5040 as the ideal number of citizens in a city as 5040 has more divisors than any numbers less than it.
Is it true that all highly composite numbers are harshad numbers?
One need only look at the three largest proper divisors of a particular highly composite number to ascertain this fact. It is false that all highly composite numbers are also Harshad numbers in base 10. The first HCN that is not a Harshad number is 245,044,800, which has a digit sum of 27, but 27 does not divide evenly into 245,044,800.
How many highly composite numbers are in the OEIS?
The initial or smallest 38 highly composite numbers are listed in the table below (sequence A002182 in the OEIS ). The number of divisors is given in the column labeled d ( n ). Asterisks indicate superior highly composite numbers . The divisors of the first 15 highly composite numbers are shown below.
What are the divisors of a highly composite number?
The number of divisors is given in the column labeled d ( n ). Asterisks indicate superior highly composite numbers . The divisors of the first 15 highly composite numbers are shown below. The table below shows all 72 divisors of 10080 by writing it as a product of two numbers in 36 different ways.