104

Previous  ... Next

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

Arithmetic Functions on $104$

\(\ds \map {\sigma_0} { 104 }\)

\(=\)

\(\ds 8\)

$\sigma_0$ of $104$

\(\ds \map \phi { 104 }\)

\(=\)

\(\ds 48\)

$\phi$ of $104$

\(\ds \map {\sigma_1} { 104 }\)

\(=\)

\(\ds 210\)

$\sigma_1$ of $104$

Also see

• Previous  ... Next: Consecutive Integers with Same Euler Phi Value

• Previous  ... Next: Sequences of 4 Consecutive Integers with Falling Divisor Sum

• Previous  ... Next: Primitive Semiperfect Number
• Previous  ... Next: Primitive Abundant Number

• Previous  ... Next: Numbers of Zeroes that Factorial does not end with

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $104$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $104$