41,616

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Number

$41,616$ (forty-one thousand, six hundred and sixteen) is:

$2^4 \times 3^2 \times 17^2$

The $4$th number after $1$, $36$, $1225$ to be both square and triangular:

$41 \, 616 = 204^2 = \dfrac {288 \times \paren {288 + 1} } 2$

The $204$th square number:

$41 \, 616 = 204 \times 204$

The $288$th triangular number:

$41 \, 616 = \ds \sum_{k \mathop = 1}^{288} k = \dfrac {288 \times \paren {288 + 1} } 2$

Also see

• Previous  ... Next: Integer both Square and Triangular
• Previous  ... Next: Square Number
• Previous  ... Next: Triangular Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1225$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1225$