168

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Number

$168$ (one hundred and sixty-eight) is:

$2^3 \times 3 \times 7$

The $1$st element of the $1$st set of $3$ integers $T$ such that $m \map {\sigma_0} m$ is equal for each $m \in T$:

$168 \times \map {\sigma_0} {168} = 192 \times \map {\sigma_0} {192} = 224 \times \map {\sigma_0} {224} = 2688$

The number of primes with no more than $3$ digits:

$2, 3, 5, 7, 11, 13, 17, 19, 23, \ldots, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997$

The $5$th positive integer after $1$, $24$, $26$, $87$ whose Euler $\phi$ value is equal to the product of its digits:

$\map \phi {168} = 48 = 1 \times 6 \times 8$

The $11$th integer $n$ after $1, 3, 15, 30, 35, 56, 70, 78, 105, 140$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:

$\map {\sigma_0} {168} = 16$, $\map \phi {168} = 48$, $\map {\sigma_1} {168} = 480$

The smallest positive integer which can be expressed as the sum of $2$ odd primes in $13$ ways.

The $25$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$, $16$, $18$, $20$, $24$, $30$, $36$, $42$, $48$, $60$, $72$, $84$, $90$, $96$, $108$, $120$, $144$:

$\map {\sigma_1} {168} = 480$

Arithmetic Functions on $168$

\(\ds \map {\sigma_0} { 168 }\)

\(=\)

\(\ds 16\)

$\sigma_0$ of $168$

\(\ds \map \phi { 168 }\)

\(=\)

\(\ds 48\)

$\phi$ of $168$

\(\ds \map {\sigma_1} { 168 }\)

\(=\)

\(\ds 480\)

$\sigma_1$ of $168$

Also see

• Previous  ... Next: Numbers of Primes with at most n Digits
• Previous  ... Next: Numbers for which Euler Phi Function equals Product of Digits
• Previous  ... Next: Smallest Positive Integer which is Sum of 2 Odd Primes in n Ways

No further terms of this sequence are documented on $\mathsf{Pr} \infty \mathsf{fWiki}$.

• Previous  ... Next: Numbers such that Divisor Count divides Phi divides Divisor Sum
• Previous  ... Next: Highly Abundant Number
• Next: Smallest Triplet of Integers whose Product with Divisor Count are Equal

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $168$