Integer both Square and Triangular/Examples

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Examples of Integer both Square and Triangular

The following integers are both square and triangular:

$n$ $\dfrac {k \paren {k + 1} } 2$ $m^2$ $a b = m$ $\dfrac a b$
$1$ $\dfrac {1 \paren {1 + 1} } 2$ $1^2$ $1 \times 1$ $1$
$36$ $\dfrac {8 \paren {8 + 1} } 2$ $6^2$ $3 \times 2$ $1 \cdotp 5$
$1225$ $\dfrac {49 \paren {49 + 1} } 2$ $35^2$ $7 \times 5$ $1 \cdotp 4$
$41 \, 616$ $\dfrac {288 \paren {288 + 1} } 2$ $204^2$ $17 \times 12$ $1 \cdotp 41 \dot 6$

This sequence is A001110 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


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