# 219

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## Number

$219$ (two hundred and nineteen) is:

$3 \times 73$

The $42$nd lucky number:
$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $163$, $169$, $171$, $189$, $193$, $195$, $201$, $205$, $211$, $219$, $\ldots$

The $35$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $130$, $133$, $139$, $167$, $176$, $188$, $190$, $192$, $193$, $203$, $208$:
$219 \to 2^2 + 1^2 + 9^2 = 4 + 1 + 81 = 86 \to 8^2 + 6^2 = 64 + 36 = 100 \to 1^2 + 0^2 + 0^2 = 1$

The $2$nd of $4$ integers $n$ such that $n + 2 n$ can be expressed as a sum using each of the digits $1$ to $9$ exactly once each:
$219 + 438 = 657$

There are $219$ Fedorov groups.