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# 49

Please do not rely on any information it contains.

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 &times 3 and 50 = 2 × 5 2.

## 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

 ${\displaystyle 3x+1}$ 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.

 ${\displaystyle {\sqrt {49}}}$ 7.00000000 49 2 2401 ${\displaystyle {\sqrt[{3}]{49}}}$ 49 3 117649 ${\displaystyle {\sqrt[{4}]{49}}}$ 2.64575131 A010465 49 4 5764801 ${\displaystyle {\sqrt[{5}]{49}}}$ 49 5 282475249 ${\displaystyle {\sqrt[{6}]{49}}}$ 1.91293118 A005482 49 6 13841287201 ${\displaystyle {\sqrt[{7}]{49}}}$ 49 7 678223072849 ${\displaystyle {\sqrt[{8}]{49}}}$ 1.62657656 A011005 49 8 33232930569601 ${\displaystyle {\sqrt[{9}]{49}}}$ 49 9 1628413597910449 ${\displaystyle {\sqrt[{10}]{49}}}$ 1.47577316 A011092 49 10 79792266297612001 ${\displaystyle {\sqrt[{11}]{7}}}$ 49 11 3909821048582988049 ${\displaystyle {\sqrt[{12}]{7}}}$ 1.38308755 A011230 49 12 191581231380566414401 A087752

## Values for number theoretic functions with 49 as an argument

 ${\displaystyle \mu (49)}$ 0 ${\displaystyle M(9)}$ −3 ${\displaystyle \pi (49)}$ ${\displaystyle \sigma _{1}(49)}$ 57 ${\displaystyle \sigma _{0}(49)}$ 3 ${\displaystyle \phi (49)}$ 42 ${\displaystyle \Omega (49)}$ 2 ${\displaystyle \omega (49)}$ 1 ${\displaystyle \lambda (49)}$ This is the Carmichael lambda function. ${\displaystyle \lambda (49)}$ 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 ${\displaystyle \mathbb {Z} }$. But it has more prime factors in some quadratic integer rings.

TABLE GOES HERE

## Representation of 49 in various bases

TABLE GOES HERE

REMARKS

 ${\displaystyle -1}$ 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