57

Number

$57$ (fifty-seven) is:

$3 \times 19$

In the smallest equilateral triangle with sides of integer length ($112$) which contains a point which is an integer distance from each vertex, the distance from that point to its nearest vertex (the other two being $65$ and $73$).

The $6$th second pentagonal number after $2$, $7$, $15$, $26$, $40$:

$57 = \dfrac {6 \paren {3 \times 6 + 1} } 2$

The $7$th integer after $7$, $13$, $19$, $35$, $38$, $41$ the decimal representation of whose square can be split into two parts which are each themselves square:

$57^2 = 3249$; $324 = 18^2$, $9 = 3^2$

The $12$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$:

$57 = \dfrac {6 \paren {3 \times 6 + 1} } 2$

The $18$th Ulam number after $1$, $2$, $3$, $4$, $6$, $8$, $11$, $13$, $16$, $18$, $26$, $28$, $36$, $38$, $47$, $48$, $53$:

$57 = 4 + 53$

The $20$th semiprime after $4$, $6$, $9$, $10$, $14$, $15$, $21$, $22$, $25$, $26$, $33$, $34$, $35$, $38$, $39$, $46$, $49$, $51$, $55$:

$57 = 3 \times 19$