# 16

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## Number

$16$ (**sixteen**) is:

- $2^4$

- The $4$th square number after $1$, $4$, $9$:
- $16 = 4 \times 4$

- The $5$th powerful number after $1$, $4$, $8$, $9$

- The $2$nd fourth power after $1$:
- $16 = 2 \times 2 \times 2 \times 2$

- The $2$nd power of $4$ after $(1)$, $4$:
- $16 = 4^2$

- The $1$st power of $16$ after the zeroth $1$:
- $16 = 16^1$

- The $9$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$:
- $\sigma \left({16}\right) = 31$

- The $9$th Ulam number after $1$, $2$, $3$, $4$, $6$, $8$, $11$, $13$:
- $16 = 3 + 13$

- The $1$st square number to be the sum of two triangular numbers in two different ways:
- $16 = 10 + 6 = 15 + 1$

- The $4$th power of $2$ after $(1)$, $2$, $4$, $8$:
- $16 = 2^4$

- The $5$th almost perfect number after $1$, $2$, $4$, $8$:
- $\sigma \left({16}\right) = 31 = 2 \times 16 - 1$

- The $6$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
- $3$, $4$, $9$, $10$, $12$, $16$, $\ldots$

- The $8$th even number after $2$, $4$, $6$, $8$, $10$, $12$, $14$ which cannot be expressed as the sum of $2$ composite odd numbers.

- The $11$th after $1$, $2$, $4$, $5$, $6$, $8$, $9$, $12$, $13$, $15$ of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes.

- The $14$th integer $n$ after $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $13$, $14$, $15$ such that $2^n$ contains no zero in its decimal representation:
- $2^{16} = 65 \, 536$

- The $11$th positive integer after $2$, $3$, $4$, $7$, $8$, $9$, $10$, $11$, $14$, $15$ which cannot be expressed as the sum of distinct pentagonal numbers.

## Also see

*Previous ... Next*: Fourth Power*Previous ... Next*: Sequence of Powers of 16

*Previous ... Next*: Squares with No More than 2 Distinct Digits*Previous ... Next*: Powerful Number*Previous ... Next*: Square Number

*Previous ... Next*: 91 is Pseudoprime to 35 Bases less than 91*Previous ... Next*: Highly Abundant Number

*Previous ... Next*: Ulam Number

*Previous ... Next*: Positive Integers Not Expressible as Sum of Distinct Non-Pythagorean Primes*Previous ... Next*: Powers of 2 with no Zero in Decimal Representation*Previous ... Next*: Numbers not Expressible as Sum of Distinct Pentagonal Numbers

## Sources

- 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 13$: The fundamental theorem of arithmetic - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $16$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $16$