16
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Number
$16$ (sixteen) is:
- $2^4$
- The $1$st power of $16$ after the zeroth $1$:
- $16 = 16^1$
- The $1$st square number to be the sum of two triangular numbers in two different ways:
- $16 = 10 + 6 = 15 + 1$
- 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 number of different binary operations that can be applied to a set with $2$ elements
- The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $3$ different ways:
- $16 = 1 + 15 = 3 + 13 = 7 + 9$
- The $4$th square number after $1$, $4$, $9$:
- $16 = 4 \times 4$
- The $4$th power of $2$ after $(1)$, $2$, $4$, $8$:
- $16 = 2^4$
- The $4$th square after $1$, $4$, $9$ which has no more than $2$ distinct digits and does not end in $0$:
- $16 = 4^2$
- The $5$th almost perfect number after $1$, $2$, $4$, $8$:
- $\map {\sigma_1} {16} = 31 = 2 \times 16 - 1$
- The $5$th powerful number after $1$, $4$, $8$, $9$
- 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 $9$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$:
- $\map {\sigma_1} {16} = 31$
- The $9$th Ulam number after $1$, $2$, $3$, $4$, $6$, $8$, $11$, $13$:
- $16 = 3 + 13$
- 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 $11$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.
- The $12$th after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $10$, $12$, $14$ of $21$ integers which can be represented as the sum of two primes in the maximum number of ways
- 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:
- $2^{16} = 65 \, 536$
Also see
- Previous ... Next: Fourth Power
- Previous ... Next: Sequence of Powers of 16
- Previous ... Next: Count of Binary Operations on Set
- 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: Integers whose Number of Representations as Sum of Two Primes is Maximum
- Previous ... Next: Positive Even Integers not Expressible as Sum of 2 Composite Odd Numbers
- 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): $16$