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80
80 is an integer, the smallest number where and are both products of 4 or more primes.
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 80
- 3 Partitions of 80
- 4 Roots and powers of 80
- 5 Logarithms and eightieth powers
- 6 Values for number theoretic functions with 80 as an argument
- 7 Factorization of some small integers in a quadratic integer ring with discriminant −80, 80
- 8 Factorization of 80 in some quadratic integer rings
- 9 Representation of 80 in various bases
- 10 See also
Membership in core sequences
Even numbers | ..., 74, 76, 78, 80, 82, 84, 86, ... | A005803 |
Composite numbers | ..., 76, 77, 78, 80, 81, 82, 84, ... | A002808 |
Abundant numbers | ..., 70, 72, 78, 80, 84, 88, 90, ... | A005101 |
Numbers that are the sum of two squares | ..., 72, 73, 74, 80, 81, 82, 85, ... | A001481 |
Sequences pertaining to 80
Divisors of 80 | 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 | A018275 |
Multiples of 80 | 80, 160, 240, 320, 400, 480, 560, 640, 720, 800, 880, 960, 1040, ... | |
sequence beginning at 15 | ..., 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ... | A033480 |
Partitions of 80
There are 15796476 partitions of 80.
The Goldbach representations of 80 are: 7 + 73 = 13 + 67 = 19 + 61 = 37 + 43.
Roots and powers of 80
In the table below, irrational numbers are given truncated to eight decimal places.
TABLE GOES HERE
Logarithms and eightieth powers
In the OEIS specifically and mathematics in general, refers to the natural logarithm of , whereas all other bases are specified with a subscript.
As above, irrational numbers in the following table are truncated to eight decimal places.
TABLE GOES HERE
Values for number theoretic functions with 80 as an argument
0 | ||
−4 | ||
22 | ||
186 | ||
10 | ||
40 | ||
5 | ||
2 | ||
4 | This is the Carmichael lambda function. | |
−1 | This is the Liouville lambda function. |
Factorization of some small integers in a quadratic integer ring with discriminant −80, 80
Since 80 is not squarefree, the of the [FINISH WRITING]
Factorization of 80 in some quadratic integer rings
In , 80 has the prime factorization of 2 4 × 5. But it has different factorizations in some quadratic integer rings.
TABLE GOES HERE
Representation of 80 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 80 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 1010000 | 2222 | 1100 | 310 | 212 | 143 | 120 | 88 | 80 | 73 | 68 | 62 | 5A | 55 | 50 | 4C | 48 | 44 | 40 |
See also
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |
30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |
1729 |