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49
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49 is the square of 7. It is the smallest positive integer which is not squarefree such that both of its neighbors are also not squarefree: 48 = 2 4 × 3 and 50 = 2 × 5 2.
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 49
- 3 Partitions of 49
- 4 Roots and powers of 49
- 5 Values for number theoretic functions with 49 as an argument
- 6 Factorization of some small integers in a quadratic integer ring adjoining the square roots of −49, 49
- 7 Factorization of 49 in some quadratic integer rings
- 8 Representation of 49 in various bases
- 9 See also
Membership in core sequences
Odd numbers | ..., 43, 45, 47, 49, 51, 53, 55, ... | A005843 |
Composite numbers | ..., 45, 46, 48, 49, 50, 51, 52, ... | A002808 |
Perfect squares | ..., 16, 25, 36, 49, 64, 81, 100, ... | A000290 |
Powers of primes | ..., 41, 43, 47, 49, 53, 59, 61, ... | A000961 |
Sequences pertaining to 49
sequence beginning at 57 | 57, 172, 86, 43, 130, 65, 196, 98, 49, 148, 74, 37, 112, ... | A008876 |
Partitions of 49
There are 173525 partitions of 49.
Roots and powers of 49
In the table below, irrational numbers are given truncated to eight decimal places.
7.00000000 | 49 2 | 2401 | ||
49 3 | 117649 | |||
2.64575131 | A010465 | 49 4 | 5764801 | |
49 5 | 282475249 | |||
1.91293118 | A005482 | 49 6 | 13841287201 | |
49 7 | 678223072849 | |||
1.62657656 | A011005 | 49 8 | 33232930569601 | |
49 9 | 1628413597910449 | |||
1.47577316 | A011092 | 49 10 | 79792266297612001 | |
49 11 | 3909821048582988049 | |||
1.38308755 | A011230 | 49 12 | 191581231380566414401 | |
A087752 |
Values for number theoretic functions with 49 as an argument
0 | ||
−3 | ||
57 | ||
3 | ||
42 | ||
2 | ||
1 | ||
This is the Carmichael lambda function. | ||
This is the Liouville lambda function. |
Factorization of some small integers in a quadratic integer ring adjoining the square roots of −49, 49
Since 49 is not squarefree, [FINISH WRITING]
Factorization of 49 in some quadratic integer rings
As was mentioned above, 49 is the square of 7 and has only one distinct prime factor in . But it has more prime factors in some quadratic integer rings.
TABLE GOES HERE
Representation of 49 in various bases
TABLE GOES HERE
REMARKS
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 |