34

Number
$34$ (thirty-four) is:
 * $2 \times 17$


 * The $4$th heptagonal number after $1, 7, 18$:
 * $34 = 1 + 7 + 11 + 16 = \dfrac {4 \left({5 \times 4 - 3}\right)} 2$


 * The $12$th semiprime after $4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33$:
 * $34 = 2 \times 17$


 * The $9$th Fibonacci number, after $1, 1, 2, 3, 5, 8, 13, 21$:
 * $34 = 13 + 21$


 * The $3$rd nontotient after $14, 26$:
 * $\nexists m \in \Z_{>0}: \phi \left({m}\right) = 34$
 * where $\phi \left({m}\right)$ denotes the Euler $\phi$ function


 * The $3$rd noncototient after $10, 26$:
 * $\nexists m \in \Z_{>0}: m - \phi \left({m}\right) = 34$
 * where $\phi \left({m}\right)$ denotes the Euler $\phi$ function


 * The smallest positive integer to be the sum of $2$ lucky numbers in $4$ different ways:
 * $34 = 1 + 33 = 3 + 31 = 9 + 25 = 13 + 21$


 * The $24$th integer $n$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{34} = 17 \, 179 \, 869 \, 184$


 * The $1$st positive integer which can be expressed as the sum of $2$ odd primes in $4$ ways:
 * $34 = 31 + 3 = 29 + 7 = 23 + 11 = 17 + 17$


 * The $4$th positive integer which cannot be expressed as the sum of a square and a prime:
 * $1, 10, 25, 34, \ldots$


 * The $2$nd non-square positive integer which cannot be expressed as the sum of a square and a prime:
 * $10, 34, \ldots$


 * The magic constant of the order $4$ magic square.
 * $34 = \dfrac {4 \left({4^2 + 1}\right)} 2$