104

Number
$104$ (one hundred and four) is:


 * $2^3 \times 13$


 * The $4$th primitive abundant number after $20$, $70$, $88$:
 * $1 + 2 + 4 + 8 + 13 + 26 + 52 = 106 > 104$


 * The $5$th primitive semiperfect number after $6$, $20$, $28$, $88$:
 * $104 = 1 + 4 + 8 + 13 + 26 + 52$


 * The $1$st of the $2$nd ordered quadruple of consecutive integers that have divisor sums which are strictly decreasing:
 * $\map {\sigma_1} {104} = 210, \ \map {\sigma_1} {105} = 192, \ \map {\sigma_1} {106} = 162, \ \map {\sigma_1} {107} = 108$


 * The $4$th positive integer solution after $1$, $3$, $15$ to $\map \phi n = \map \phi {n + 1}$:
 * $\map \phi {104} = 48 = \map \phi {105}$


 * The $20$th positive integer $n$ after $5$, $11$, $17$, $23$, $29$, $30$, $36$, $42$, $48$, $54$, $60$, $61$, $67$, $73$, $79$, $85$, $91$, $92$, $98$ such that no factorial of an integer can end with $n$ zeroes

Also see