Natural number
34 (thirty-four) is thenatural number following33 and preceding35 .
34 is the twelfthsemiprime ,[ 1] divisors including1 and itself. Specifically, 34 is the ninth distinctsemiprime , it being the sixth of the form2 × q {\displaystyle 2\times q} 33 and35 are also distinct semiprimes with four divisors each, where 34 is the smallest number to be surrounded by numbers with the same number of divisors it has. This is the first distinct semiprime treble cluster, the next being (85 ,86 ,87 ).[ 2]
34 is the sum of the first twoperfect numbers 6 +28 ,[ 3] composite index (22 ).[ 4]
Itsreduced totient andEuler totient values are both 16 (or 42 = 24 ).[ 5] [ 6] 53 , which is the sixteenth prime number.
There is no solution to the equationφ (x ) = 34, making 34 anontotient .[ 7] x − φ(x ) = 34, making 34 anoncototient .[ 8]
It is the thirdErdős–Woods number , following22 and16 .[ 9]
It is the ninthFibonacci number [ 10] Pell number .[ 11] Markov number .[ 12]
34 is also the fourthheptagonal number ,[ 13] centered hendecagonal (11-gonal) number.[ 14]
This number is also themagic constant ofn − {\displaystyle n-} Queens Problem forn = 4 {\displaystyle n=4} [ 15]
There are 34topologically distinct convex heptahedra , excluding mirror images.[ 16]
34 is themagic constant of a4 × 4 {\displaystyle 4\times 4} magic square ,[ 17] magic octagram (see accompanying images); it is the onlyn {\displaystyle n} n × n {\displaystyle n\times n}
^ Sloane, N. J. A. (ed.)."Sequence A001358 (Semiprimes (or biprimes): products of two primes)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A056809 (Numbers k such that k, k+1 and k+2 are products of two primes)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A02808 (The composite numbers.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2024-06-02 .^ Sloane, N. J. A. (ed.)."Sequence A000010 (Euler totient function phi(n): count numbers less than and equal to n and prime to n.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2023-09-11 .^ Sloane, N. J. A. (ed.)."Sequence A002322 (Reduced totient function psi(n): least k such that x^k congruent to 1 (mod n) for all x prime to n; also known as the Carmichael lambda function (exponent of unit group mod n); also called the universal exponent of n)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A005277 (Nontotients)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A005278 (Noncototients)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A059756 (Erdős–Woods numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A000045 (Fibonacci numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A002203 (Companion Pell numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Weisstein, Eric W."Markov Number" .mathworld.wolfram.com . Retrieved2020-08-21 . ^ Sloane, N. J. A. (ed.)."Sequence A000566 (Heptagonal numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A069125 (Centered hendecagonal (11-gonal) numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A006003 (a(n) = n*(n^2 + 1)/2)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ "Counting polyhedra" .Numericana . Retrieved2022-04-20 .^ Higgins, Peter (2008).Number Story: From Counting to Cryptography . New York: Copernicus. p. 53.ISBN 978-1-84800-000-1
400 to 999
400s, 500s, and 600s 700s, 800s, and 900s
1000s and 10,000s
1000s 10,000s
100,000s to 10,000,000,000,000s
100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000
