310
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Number
$310$ (three hundred and ten) is:
- $2 \times 5 \times 31$
- The $16$th number after $1$, $3$, $22$, $66$, $70$, $81$, $94$, $115$, $119$, $170$, $210$, $214$, $217$, $265$, $282$ whose divisor sum is square:
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- $\map {\sigma_1} {310} = 576 = 24^2$
- The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $19$ different ways
- The $31$st noncototient after $10$, $26$, $34$, $50$, $\ldots$, $244$, $260$, $266$, $268$, $274$, $290$, $292$, $298$:
- $\nexists m \in \Z_{>0}: m - \map \phi m = 310$
- where $\map \phi m$ denotes the Euler $\phi$ function
- The $33$rd sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $246$, $255$, $258$, $266$, $273$, $282$, $285$, $286$, $290$:
- $310 = 2 \times 5 \times 31$
- The $47$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $226$, $230$, $236$, $239$, $262$, $263$, $280$, $291$, $293$, $301$, $302$:
- $310 \to 3^2 + 1^2 + 0^2 = 9 + 1 + 0 = 10 \to 1^2 + 0^2 = 1$