126

Number
$126$ (one hundred and twenty-six) is:


 * $2 \times 3^2 \times 7$


 * The $6$th pentagonal pyramidal number after $1$, $6$, $12$, $40$, $75$:
 * $126 = 1 + 5 + 12 + 22 + 35 + 51 = \dfrac {6^2 \paren {6 + 1} } 2$


 * The $9$th second pentagonal number after $2$, $7$, $15$, $26$, $40$, $57$, $77$, $100$:
 * $126 = \dfrac {9 \paren {3 \times 9 + 1} } 2$


 * The $18$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$, $57$, $70$, $77$, $92$, $100$, $117$:
 * $126 = \dfrac {9 \paren {3 \times 9 + 1} } 2$


 * The $6$th pentatope number after $1$, $5$, $15$, $35$, $70$:
 * $126 = 1 + 4 + 10 + 20 + 35 + 56 = \dfrac {6 \paren {6 + 1} \paren {6 + 2} \paren {6 + 3} } {24}$


 * The $4$th even integer after $98$, $122$, $124$ that cannot be expressed as the sum of $2$ prime numbers of which the smaller one is $3$, $5$ or $7$.