147

Previous  ... Next

Number

$147$ (one hundred and forty-seven) is:

$3 \times 7^2$

The $3$rd term of the $3$rd $5$-tuple of consecutive integers have the property that they are not values of the divisor sum function $\map {\sigma_1} n$ for any $n$:

$\tuple {145, 146, 147, 148, 149}$

The number of different representations of $1$ as the sum of $5$ unit fractions.

The $1$st of the $5$th pair of consecutive integers which both have $6$ divisors:

$\map {\sigma_0} {147} = \map {\sigma_0} {148} = 6$

The $28$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.

The $60$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $95$, $96$, $100$, $101$, $102$, $107$, $112$, $116$, $124$, $136$, $137$, $141$, $142$ which cannot be expressed as the sum of distinct pentagonal numbers.

$42 \times 147 = 6174$ which is Kaprekar's Constant

Also see

• Previous  ... Next: Representation of 1 as Sum of n Unit Fractions
• Previous  ... Next: Pairs of Consecutive Integers with 6 Divisors
• Previous  ... Next: Numbers of Zeroes that Factorial does not end with
• Previous  ... Next: Numbers not Expressible as Sum of Distinct Pentagonal Numbers
• Previous  ... Next: Quintuplets of Consecutive Integers which are not Divisor Sum Values

Historical Note

$147$ is of course the maximum break in a game of snooker.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $147$