325
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Number
$325$ (three hundred and twenty-five) is:
- $5^2 \times 13$
- The $1$st positive integer which can be expressed as the sum of two square numbers in $3$ distinct ways:
- $325 = 18^2 + 1^2 = 17^2 + 6^2 = 15^2 + 10^2$
- The total of all the entries in a magic square of order $5$, after $1$, $(10)$, $45$, $136$:
- $325 = \ds \sum_{k \mathop = 1}^{5^2} k = \dfrac {5^2 \paren {5^2 + 1} } 2$
- The total number of permutations of $r$ objects from a set of $5$ objects, where $1 \le r \le 5$
- The $10$th positive integer after $200$, $202$, $204$, $205$, $206$, $208$, $320$, $322$, $324$ that cannot be made into a prime number by changing just $1$ digit
- The $13$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $120$, $153$, $190$, $231$, $276$:
- $325 = \ds \sum_{k \mathop = 1}^{13} \paren {4 k - 3} = 13 \paren {2 \times 13 - 1}$
- The $25$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $171$, $190$, $210$, $231$, $253$, $276$, $300$:
- $325 = \ds \sum_{k \mathop = 1}^{25} k = \dfrac {25 \times \paren {25 + 1} } 2$
Also see
- Previous ... Next: Count of All Permutations on n Objects
- Previous ... Next: Sum of Terms of Magic Square
- Previous ... Next: Hexagonal Number
- Previous ... Next: Triangular Number
- Previous ... Next: Numbers that cannot be made Prime by changing 1 Digit
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $325$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $325$