# 147

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## 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 $\sigma$ function $\map \sigma n$ 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:
$\map \tau {147} = \map \tau {148} = 6$

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.