90

Number
$90$ (ninety) is:


 * $2 \times 3^2 \times 5$


 * The $20$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$, $16$, $18$, $20$, $24$, $30$, $36$, $42$, $48$, $60$, $72$, $84$:
 * $\sigma \left({90}\right) = 234$


 * The $11$th nontotient after $14$, $26$, $34$, $38$, $50$, $62$, $68$, $74$, $76$, $86$:
 * $\nexists m \in \Z_{>0}: \phi \left({m}\right) = 90$
 * where $\phi \left({m}\right)$ denotes the Euler $\phi$ function


 * The $21$st semiperfect number after $6$, $12$, $18$, $20$, $24$, $28$, $30$, $36$, $40$, $42$, $48$, $54$, $56$, $60$, $66$, $72$, $78$, $80$, $84$, $88$:
 * $90 = 15 + 30 + 45$


 * The $3$rd unitary perfect number after $6$, $60$:
 * $90 = 1 + 2 + 5 + 9 + 10 + 18 + 45$


 * The smallest positive integer which can be expressed as the sum of $2$ odd primes in $9$ ways.


 * The $4$th element of the $1$st set of $4$ positive integers which form an arithmetic progression which all have the same Euler $\phi$ value:
 * $\phi \left({72}\right) = \phi \left({78}\right) = \phi \left({84}\right) = \phi \left({90}\right) = 24$