# 226

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## Number

$226$ (two hundred and twenty-six) is:

$2 \times 113$

The $36$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $130$, $133$, $139$, $167$, $176$, $188$, $190$, $192$, $193$, $203$, $208$, $219$:
$226 \to 2^2 + 2^2 + 6^2 = 4 + 4 + 36 = 44 \to 4^2 + 4^2 = 16 + 16 = 32 \to 3^2 + 2^2 = 9 + 4 = 13 \to 1^2 + 3^2 = 9 + 1 = 10 \to 1^2 + 0^2 = 1$

The $14$th positive integer which cannot be expressed as the sum of a square and a prime:
$1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $214$, $226$, $\ldots$

The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $14$ different ways

The $8$th non-square positive integer which cannot be expressed as the sum of a square and a prime:
$10$, $34$, $58$, $85$, $91$, $130$, $214$, $226$, $\ldots$