Examples
The highly composite number : 10,080. 10,080 = (2 × 2 × 2 × 2 × 2) × (3 × 3) × 5 × 7 By (2) above, 10,080 has exactly seventy-two divisors. |
|||||
1 × 10,080 |
2 × 5,040 |
3 × 3,360 |
4 × 2,520 |
5 × 2,016 |
6 × 1,680 |
7 × 1,440 |
8 × 1,260 |
9 × 1,120 |
10 × 1,008 |
12 × 840 |
14 × 720 |
15 × 672 |
16 × 630 |
18 × 560 |
20 × 504 |
21 × 480 |
24 × 420 |
28 × 360 |
30 × 336 |
32 × 315 |
35 × 288 |
36 × 280 |
40 × 252 |
42 × 240 |
45 × 224 |
48 × 210 |
56 × 180 |
60 × 168 |
63 × 160 |
70 × 144 |
72 × 140 |
80 × 126 |
84 × 120 |
90 × 112 |
96 × 105 |
Note: The bolded numbers are themselves highly composite numbers. Only the twentieth highly composite number 7560 (= 3 × 2520) is absent. |
10080 is a so-called 7-smooth number, (sequence A002473 in OEIS). |
The 15,000th highly composite number can be found on Achim Flammenkamp's website. It is the product of 230 primes:
where is the sequence of successive prime numbers, and all omitted terms (a22 to a228) are factors with exponent equal to one (i.e. the number is ).
Read more about this topic: Highly Composite Number
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold peoples attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (18961966)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (15331592)