364

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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:

$\map {\sigma_1} {364} = 784 = 28^2$

Also see

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