40

Number
$40$ (forty) is:


 * $2^3 \times 5$


 * The only number whose name in the English language has all its letters in alphabetical order:
 * forty


 * The $4$th octagonal number, after $1$, $8$, $21$:
 * $40 = 1 + 7 + 13 + 19 = 4 \paren {3 \times 4 - 2}$


 * The $4$th pentagonal pyramidal number after $1$, $6$, $18$:
 * $40 = 1 + 5 + 12 + 22 = \dfrac {4^2 \paren {4 + 1} } 2$


 * The $5$th second pentagonal number after $2$, $7$, $15$, $26$:
 * $40 = \dfrac {5 \paren {3 \times 5 + 1} } 2$


 * The $7$th abundant number after $12, 18, 20, 24, 30, 36$:
 * $1 + 2 + 4 + 5 + 8 + 10 + 20 = 50 > 40$


 * The $9$th semiperfect number after $6$, $12$, $18$, $20$, $24$, $28$, $30$, $36$:
 * $40 = 2 + 8 + 10 + 20$


 * The $10$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$:
 * $40 = \dfrac {5 \paren {3 \times 5 + 1} } 2$


 * The $16$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
 * $3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $\ldots$


 * The $19$th harshad number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $10$, $12$, $18$, $20$, $21$, $24$, $27$, $30$, $36$:
 * $40 = 10 \times 4 = 10 \times \paren {4 + 0}$

Also see