176

Number
$176$ (one hundred and seventy-six) is:
 * $2^4 \times 11$


 * The $11$th pentagonal number after $1, 5, 12, 22, 35, 51, 70, 92, 117, 145$:
 * $176 = 1 + 4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 + 31 = \dfrac {11 \left({3 \times 11 - 1}\right)} 2$


 * The $21$st generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$, $57$, $70$, $77$, $92$, $100$, $117$, $126$, $145$, $155$:
 * $176 = \dfrac {11 \left({3 \times 11 - 1}\right)} 2$


 * The $8$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $96$, $133$:
 * $176 = 1 + 7 + 13 + 19 + 25 + 31 + 37 + 43 = 8 \left({3 \times 8 - 2}\right)$


 * The $28$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $91$, $94$, $97$, $100$, $103$, $109$, $129$, $130$, $133$, $139$, $167$:
 * $176 \to 1^2 + 7^2 + 6^2 = 1 + 49 + 36 = 86 \to 8^2 + 6^2 = 64 + 36 = 100 \to 1^2 + 0^2 + 0^2 = 1$