32
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Number
$32$ (thirty-two) is:
- $2^5$
- In binary:
- $100 \, 000$
- The $2$nd fifth power after $1$:
- $32 = 2 \times 2 \times 2 \times 2 \times 2$
- The $2$nd element of the $2$nd pair of integers $m$ whose values of $m \map {\sigma_0} m$ is equal:
- $24 \times \map {\sigma_0} {24} = 192 = 32 \times \map {\sigma_0} {32}$
- The $5$th power of $2$ after $(1)$, $2$, $4$, $8$, $16$:
- $32 = 2^5$
- The $6$th almost perfect number after $1$, $2$, $4$, $8$, $16$:
- $\map {\sigma_1} {32} = 63 = 2 \times 32 - 1$
- The $8$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $27$
- The $8$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
- $3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$
- The $9$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $28$, $31$:
- $32 \to 3^2 + 2^2 = 9 + 4 = 13 \to 1^2 + 3^2 = 9 + 1 = 10 \to 1^2 + 0^2 = 1$
- The $13$th even number after $2$, $4$, $6$, $8$, $10$, $12$, $14$, $16$, $20$, $22$, $26$, $28$ which cannot be expressed as the sum of $2$ composite odd numbers.
- The $17$th positive integer which is not the sum of $1$ or more distinct squares:
- $2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $23$, $24$, $27$, $28$, $31$, $32$, $\ldots$
- The $18$th after $1$, $2$, $4$, $5$, $6$, $8$, $9$, $12$, $13$, $15$, $16$, $17$, $20$, $24$, $25$, $27$, $28$ of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes.
- The $21$st positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $26$, $29$, $30$, $31$ which cannot be expressed as the sum of distinct pentagonal numbers.
- The $22$nd integer $n$ such that $2^n$ contains no zero in its decimal representation:
- $2^{32} = 4 \, 294 \, 967 \, 296$
- The $24$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $20$, $21$, $24$, $25$, $26$, $27$, $30$, $31$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$:There exist $32$ distinct point groups.
- There exist $32$ distinct point groups.
Also see
- Previous ... Next: Powerful Number
- Previous ... Next: Positive Integers Not Expressible as Sum of Distinct Non-Pythagorean Primes
- Previous ... Next: Positive Even Integers not Expressible as Sum of 2 Composite Odd Numbers
- Previous ... Next: Powers of 2 with no Zero in Decimal Representation
- Previous ... Next: Numbers not Sum of Distinct Squares
- Previous ... Next: Numbers not Expressible as Sum of Distinct Pentagonal Numbers
- Previous ... Next: Integers not Expressible as Sum of Distinct Primes of form 6n-1
- Previous ... Next: Happy Number
Historical Note
$32 \fahr$ is the melting point of water on the Fahrenheit scale.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $32$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $32$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): crystallography
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): crystallography