526

Number

$526$ (five hundred and twenty-six) is:

$2 \times 263$

The $10$th non-square positive integer which cannot be expressed as the sum of a square and a prime:

$10$, $34$, $58$, $85$, $91$, $130$, $214$, $226$, $370$, $526$, $\ldots$

The $19$th positive integer which cannot be expressed as the sum of a square and a prime:

$1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $214$, $226$, $289$, $324$, $370$, $400$, $526$, $\ldots$

The $22$nd Smith number after $4$, $22$, $27$, $58$, $\ldots$, $346$, $355$, $378$, $382$, $391$, $438$, $454$, $483$, $517$:

$5 + 2 + 6 = 2 + 2 + 6 + 3 = 13$

The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $27$ different ways