# 196

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## Number

$196$ (one hundred and ninety-six) is:

$2^2 \times 7^2$

The $1$st candidate Lychrel number.

The $2$nd power of $14$ after $(1)$, $14$:
$196 = 14^2$

The $6$th heptagonal pyramidal number after $1$, $8$, $26$, $60$, $115$:
$196 = 1 + 7 + 18 + 34 + 55 + 81 = \dfrac {6 \paren {6 + 1} \paren {5 \times 6 - 2} } 6$
and the $2$nd after $1$ which is square

The $7$th pentagonal pyramidal number after $1$, $6$, $12$, $40$, $75$, $126$:
$196 = 1 + 5 + 12 + 22 + 35 + 51 + 70 = \dfrac {7^2 \paren {7 + 1} } 2$
and the $2$nd after $1$ which is square

The $12$th positive integer which cannot be expressed as the sum of a square and a prime:
$1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $\ldots$

The $14$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $100$, $121$, $144$, $169$:
$196 = 14 \times 14$

The $22$nd powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $27$, $32$, $36$, $49$, $64$, $72$, $81$, $100$, $108$, $121$, $125$, $128$, $144$, $169$