130

Number
$130$ (one hundred and thirty) is:


 * $2 \times 5 \times 13$


 * The magic constant of a magic cube of order $4$, after $1$, $(9)$, $42$:
 * $130 = \displaystyle \dfrac 1 {4^2} \sum_{k \mathop = 1}^{4^3} k = \dfrac {4 \paren {4^3 + 1} } 2$


 * The $5$th positive integer after $50$, $65$, $85$, $125$ which can be expressed as the sum of two square numbers in two or more different ways:
 * $130 = 11^2 + 3^2 = 9^2 + 7^2$


 * The $6$th non-square positive integer which cannot be expressed as the sum of a square and a prime:
 * $10$, $34$, $58$, $85$, $91$, $130$, $\ldots$


 * The $10$th sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$, $114$:
 * $130 = 2 \times 5 \times 13$


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


 * The $11$th noncototient after $10$, $26$, $34$, $50$, $52$, $58$, $86$, $100$, $116$, $122$:
 * $\nexists m \in \Z_{>0}: m - \map \phi m = 130$
 * where $\map \phi m$ denotes the Euler $\phi$ function


 * The $11$th integer after $7$, $13$, $19$, $35$, $38$, $41$, $57$, $65$, $70$, $125$ the decimal representation of whose square can be split into two parts which are each themselves square:
 * $130^2 = 16 \, 900$; $16 = 4^2$, $900 = 30^2$


 * The $24$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $91$, $94$, $97$, $100$, $103$, $109$, $129$:
 * $130 \to 1^2 + 3^2 + 0^2 = 1 + 9 + 0 = 10 \to 1^2 + 0^2 = 1$