364
Jump to navigation
Jump to search
Number
$364$ (three hundred and sixty-four) is:
- $2^2 \times 7 \times 13$
- The $12$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $56$, $84$, $120$, $165$, $220$, $286$:
- $364 = \ds \sum_{k \mathop = 1}^{12} \frac {k \paren {k + 1} } 2 = \dfrac {12 \paren {12 + 1} \paren {12 + 2} } 6$
- Hence the total number of gifts in The Twelve Days of Christmas.
- The $21$st number whose divisor sum is square:
-
- $\map {\sigma_1} {364} = 784 = 28^2$