1365

Number
$1365$ (one thousand, three hundred and sixty-five) is:
 * $3 \times 5 \times 7 \times 13$


 * The $12$th pentatope number after $1$, $5$, $15$, $35$, $70$, $126$, $210$, $330$, $495$, $715$, $1001$:
 * $1365 = \ds \sum_{k \mathop = 1}^{12} \dfrac {k \paren {k + 1} \paren {k + 2} } 6 = \dfrac {12 \paren {12 + 1} \paren {12 + 2} \paren {12 + 3} } {24}$


 * The $30$th second pentagonal number after $2$, $7$, $15$, $26$, $\ldots$, $610$, $672$, $737$, $805$, $876$, $950$, $1027$, $1107$, $1190$, $1276$:
 * $1365 = \dfrac {30 \paren{3 \times 30 + 1} } 2$


 * The $60$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $925$, $950$, $1001$, $1027$, $1080$, $1107$, $1162$, $1190$, $1247$, $1276$, $1335$:
 * $1365 = \dfrac {30 \paren {3 \times 30 + 1} } 2$