133

Number
$133$ (one hundred and thirty-three) is:
 * $7 \times 19$


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


 * The $28$th lucky number:
 * $1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $63$, $67$, $73$, $75$, $79$, $87$, $93$, $99$, $105$, $111$, $115$, $127$, $129$, $133$, $\ldots$


 * The $25$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $91$, $94$, $97$, $100$, $103$, $109$, $129$, $130$:
 * $133 \to 1^2 + 3^2 + 3^2 = 1 + 9 + 9 = 19 \to 1^2 + 9^2 = 1 + 81 = 82 \to 8^2 + 2^2 = 64 + 4 = 68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$


 * One of the prime factors of one of the terms of one of the $2$ representations of $635 \, 318 \, 657$ as the sum of $2$ fourth powers:
 * $635 \, 318 \, 657 = 133^4 + 134^4$