672
Jump to navigation
Jump to search
Number
$672$ (six hundred and seventy-two) is:
- $2^5 \times 3 \times 7$
- The $2$nd triperfect number after $120$:
- $\map {\sigma_1} {672} = 2016 = 3 \times 672$
- The $7$th Ore number after $1$, $6$, $28$, $140$, $270$, $496$:
- $\dfrac {672 \times \map {\sigma_0} {672} } {\map {\sigma_1} {672} } = 8$
- and the $5$th after $1$, $6$, $14$, $270$ whose divisors also have an arithmetic mean which is an integer:
- $\dfrac {\map {\sigma_1} {672} } {\map {\sigma_0} {672} } = 84$
- The $14$th positive integer after $128$, $192$, $256$, $288$, $320$, $384$, $432$, $448$, $480$, $512$, $576$, $640$, $648$ with $7$ or more prime factors:
- $672 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 7$
- The $21$st second pentagonal number after $2$, $7$, $15$, $26$, $\ldots$, $222$, $260$, $301$, $345$, $392$, $442$, $495$, $551$, $610$:
- $672 = \dfrac {21 \paren {3 \times 21 + 1} } 2$
- The $32$nd Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $\ldots$, $216$, $224$, $312$, $315$, $384$, $432$, $612$, $624$:
- $672 = 8 \times 84 = 8 \times \paren {6 \times 7 \times 2}$
- The $42$nd generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $392$, $425$, $442$, $477$, $495$, $532$, $551$, $590$, $610$, $651$:
- $672 = \dfrac {21 \paren {3 \times 21 + 1} } 2$
Arithmetic Functions on $672$
\(\ds \map {\sigma_0} { 672 }\) | \(=\) | \(\ds 24\) | $\sigma_0$ of $672$ | |||||||||||
\(\ds \map {\sigma_1} { 672 }\) | \(=\) | \(\ds 2016\) | $\sigma_1$ of $672$ |
Also see
- Previous ... Next: Triperfect Number
- Previous ... Next: Sequence of Numbers with Integer Arithmetic and Harmonic Means of Divisors
- Previous ... Next: Ore Number
- Previous ... Next: Second Pentagonal Number
- Previous ... Next: Zuckerman Number
- Previous ... Next: Numbers with 7 or more Prime Factors
- Previous ... Next: Generalized Pentagonal Number
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $672$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $672$