2520

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Number

$2520$ (two thousand, five hundred and twenty) is:

$2^3 \times 3^2 \times 5 \times 7$

and so is the lowest common multiple of all the digits from $1$ to $9$

The smallest EPORN:

$2520 = 210 \times 012 = 120 \times 021$

The $6$th and last special highly composite number after $1$, $2$, $6$, $12$, $60$

The $18$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$, $1680$:

$\map {\sigma_0} {2520} = 48$

The $18$th superabundant number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$, $1680$:

$\dfrac {\map {\sigma_1} {2520} } {2520} = \dfrac {9360} {2520} \approx 3 \cdotp 714$

The sum of $4$ of its divisors in $6$ different ways:

\(\ds \qquad \ \ \)

\(\ds 2520\)

\(=\)

\(\ds 1260 + 630 + 504 + 126\)

\(\ds \)

\(=\)

\(\ds 1260 + 630 + 421 + 210\)

\(\ds \)

\(=\)

\(\ds 1260 + 840 + 360 + 60\)

\(\ds \)

\(=\)

\(\ds 1260 + 840 + 315 + 105\)

\(\ds \)

\(=\)

\(\ds 1260 + 840 + 280 + 140\)

\(\ds \)

\(=\)

\(\ds 1260 + 840 + 252 + 168\)

Arithmetic Functions on $2520$

\(\ds \map {\sigma_0} { 2520 }\)

\(=\)

\(\ds 48\)

$\sigma_0$ of $2520$

\(\ds \map {\sigma_1} { 2520 }\)

\(=\)

\(\ds 9360\)

$\sigma_1$ of $2520$

Also see

• EPORN/Examples/2520

• 2520 equals Sum of 4 Divisors in 6 Ways

• Previous: Special Highly Composite Number
• Previous  ... Next: Highly Composite Number
• Previous  ... Next: Superabundant Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2520$
• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The Ladies' Diary or Woman's Almanac, $\text {1704}$ – $\text {1841}$: $140$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2520$