7,906,276
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Number
$7 \, 906 \, 276$ (seven million, nine hundred and six thousand, two hundred and seventy-six) is:
- $2^2 \times 7 \times 41 \times 71 \times 97$
- The $4$th integer after $1$, $210$, $40 \, 755$ to be both pentagonal and triangular
- The $2296$th pentagonal number:
- $7 \, 906 \, 276 = \ds \sum_{k \mathop = 1}^{2296} \paren {3 k - 2} = \dfrac {2296 \paren {3 \times 2296 - 1} } 2$
- The $3976$th triangular number:
- $7 \, 906 \, 276 = \ds \sum_{k \mathop = 1}^{3976} k = \dfrac {3976 \times \paren {3976 + 1} } 2$
- The $4951$st generalized pentagonal number:
- $7 \, 906 \, 276 = \ds \sum_{k \mathop = 1}^{2296} \paren {3 k - 2} = \dfrac {2296 \paren {3 \times 2296 - 1} } 2$