# 262

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## Number

$262$ (two hundred and sixty-two) is:

$2 \times 131$

The $2$nd positive integer $n$ after $157$ for which $\map \phi {2 n + 1} < \map \phi {2 n}$:
$\map \phi {2 \times 262 + 1} = 240$, $\map \phi {2 \times 262} = 260$

The $17$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $146$, $162$, $188$, $206$, $210$, $216$, $238$, $246$, $248$

The $40$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $188$, $190$, $192$, $193$, $203$, $208$, $219$, $226$, $230$, $236$, $239$:
$262 \to 2^2 + 6^2 + 2^2 = 4 + 36 + 4 = 44 \to 4^2 + 4^2 = 16 + 16 = 32 \to 3^2 + 2^2 = 9 + 4 = 13 \to 1^2 + 3^2 = 9 + 1 = 10 \to 1^2 + 0^2 = 1$