60

Number
$60$ (Sixty) is:


 * $2^2 \times 3 \times 5$


 * The $4$th heptagonal pyramidal number after $1$, $8$, $26$:
 * $60 = 1 + 7 + 18 + 34 = \dfrac {4 \left({4 + 1}\right) \left({5 \times 4 - 2}\right)} 6$


 * The $9$th highly composite number after $1, 2, 4, 6, 12, 24, 36, 48$:
 * $\tau \left({60}\right) = 12$


 * The $17$th highly abundant number after $1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48$:
 * $\sigma \left({60}\right) = 168$


 * The $9$th superabundant number after $1, 2, 4, 6, 12, 24, 36, 48$:
 * $\dfrac {\sigma \left({60}\right)} {60} = \dfrac {168} {60} = 2 \cdotp 8$


 * The $14$th semiperfect number after $6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56$:
 * $60 = 10 + 20 + 30$


 * The base of the sexagesimal system.


 * The number of degrees in an internal angle of an equilateral triangle.


 * The smallest positive integer which is the sum of $2$ odd primes in $6$ different ways.


 * The smallest positive integer which can be expressed as the sum of $2$ odd primes in $6$ ways:
 * $60 = 7 + 53 = 13 + 47 = 17 + 43 = 19 + 41 = 23 + 37 = 29 + 31$


 * The $11$th positive integer $n$ after $5, 11, 17, 23, 29, 30, 36, 42, 48, 54$ such that no factorial of an integer can end with $n$ zeroes.


 * The $23$rd positive integer which is not the sum of $1$ or more distinct squares:
 * $2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $23$, $24$, $27$, $28$, $31$, $32$, $33$, $43$, $44$, $47$, $48$, $60$, $\ldots$


 * The $35$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $44$, $45$, $46$, $49$, $50$, $54$, $55$, $59$ which cannot be expressed as the sum of distinct pentagonal numbers.

Also see

 * Smallest Positive Integer which is Sum of 2 Odd Primes in 6 Ways