406

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Number

$406$ (four hundred and six) is:

$2 \times 7 \times 29$

The $1$st term of the $1$st sequence of $3$ consecutive triangular numbers all of which are sphenic:

\(\ds \quad \ \ \)

\(\ds T_{28}\)

\(=\)

\(\ds 406\)

\(\ds = 2 \times 7 \times 29\)

which is sphenic

\(\ds T_{29}\)

\(=\)

\(\ds 435\)

\(\ds = 3 \times 5 \times 29\)

which is sphenic

\(\ds T_{30}\)

\(=\)

\(\ds 465\)

\(\ds = 3 \times 5 \times 31\)

which is sphenic

The $28$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $171$, $190$, $210$, $231$, $253$, $276$, $300$, $325$, $351$, $378$:

$406 = \ds \sum_{k \mathop = 1}^{28} k = \dfrac {28 \times \paren {28 + 1} } 2$

The $31$st untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $324$, $326$, $336$, $342$, $372$

The $45$th sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $290$, $310$, $318$, $322$, $345$, $354$, $357$, $366$, $370$, $374$, $385$, $399$, $402$:

$406 = 2 \times 7 \times 29$

Also see

• Sequence of Smallest 3 Consecutive Triangular Numbers which are Sphenic

• Next: Sequences of 3 Consecutive Triangular Numbers which are Sphenic

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