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# 34 (number)

34 (thirty-four) is the natural number following 33 and preceding 35.

## In mathematics

34 is the ninth distinct biprime and has four divisors including unity and itself. Its neighbors, 33 and 35 also are distinct biprimes having four divisors each, and 34 is the smallest number to be surrounded by numbers with the same number of divisors as it has. It is also in the first cluster of three distinct biprime, being within; 33,34,35, the next such cluster of biprimes is; 85,86,87.

It is the ninth Fibonacci number and a companion Pell number. Since it is an odd-indexed Fibonacci number, 34 is a Markov number, appearing in solutions with other Fibonacci numbers, such as (1, 13, 34), (1, 34, 89), etc.

This number is the magic constant of a 4 by 4 normal magic square

This number is also the magic constant of n-Queens Problem for n = 4.

Thirty-four is a heptagonal number.

It has the aliquot sum, 20, in the following descending sequence 34,20,22,14,10,8,7,1. and it is the 6th composite member of the 7-aliquot tree.

There is no answer to the equation φ(x) = 34, making 34 a nontotient. Nor is there an answer to the equation x - φ(x) = 34, making 34 a noncototient.

34 is also:

## Historical years

34 A.D., 34 B.C., 1934, 2034, etc.

## References

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