100

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Number

$100$ (one hundred or a hundred) is:

$2^2 \times 5^2$


The sum of the first $4$ cubes:
$100 = 1^3 + 2^3 + 3^3 + 4^3$


The $2$nd power of $10$ after $(1)$, $10$:
$100 = 10^2$


The $4$th after $2$, $5$ and $10$ of $4$ numbers whose letters, when spelt in French, are in alphabetical order:
cent


The $8$th second pentagonal number after $2$, $7$, $15$, $26$, $40$, $57$, $77$:
$100 = \dfrac {8 \paren {3 \times 8 + 1} } 2$


The $8$th noncototient after $10$, $26$, $34$, $50$, $52$, $58$, $86$:
$\nexists m \in \Z_{>0}: m - \map \phi m = 100$
where $\map \phi m$ denotes the Euler $\phi$ function


The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $9$ different ways


The $10$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$:
$100 = 10 \times 10$


The $14$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $27$, $32$, $36$, $49$, $64$, $72$, $81$


The $16$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$, $57$, $70$, $77$, $92$:
$100 = \dfrac {8 \paren {3 \times 8 + 1} } 2$


The $20$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $28$, $31$, $32$, $44$, $49$, $68$, $70$, $79$, $82$, $86$, $91$, $94$, $97$:
$100 \to 1^2 + 0^2 + 0^2 = 1$


The $23$rd semiperfect number after $6$, $12$, $18$, $20$, $24$, $28$, $30$, $36$, $40$, $42$, $48$, $54$, $56$, $60$, $66$, $72$, $78$, $80$, $84$, $88$, $90$, $96$:
$100 = 5 + 20 + 25 + 50$


The $49$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $61$, $65$, $66$, $67$, $72$, $77$, $80$, $81$, $84$, $89$, $94$, $95$, $96$ which cannot be expressed as the sum of distinct pentagonal numbers.


Also see


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


Historical Note

The number $100$ (one hundred) was at one time sometimes referred to in England as a short hundred.

This was to distinguish it from the term long hundred for the number $120$.

Both terms are now obsolete in England, although the term great hundred for $120$ is still used in Germany and Scandinavia.


The boiling point of water is defined as being $100$ degrees Celsius.


The number $100$ is expressed in Roman numerals as $\mathrm C$.

This originates from the first letter of the Latin word centum, meaning $100$.


The archetypal "big number", to small children, is $100$. This most likely stems from the fact that their first introduction to numbers is the exercise to count to $100$. As this is where the count stops, $100$ is the biggest number they know.

Once introduced to the concept of one hundred and one, however, their level of arithmetical sophistication is soon seen to increase.


Linguistic Note

The Latin word for $100$ was centum.

Hence the prefix centi- was adopted in the metric system to mean a hundredth part.

For example, a centimetre is one hundredth part of a metre.


Sources

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