69

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Number

$69$ (sixty-nine) is:

$3 \times 23$

The only integer whose square and cube use each of the digits from $0$ to $9$ exactly once each:

$69^2 = 4761$, $69^3 = 328 \, 509$

The $4$th after $21$, $29$, $61$ of the $5$ $2$-digit positive integers which can occur as a $5$-fold repetition at the end of a square number

The $20$th Ulam number after $1$, $2$, $3$, $4$, $6$, $8$, $11$, $13$, $16$, $18$, $26$, $28$, $36$, $38$, $47$, $48$, $53$, $57$, $62$:

$69 = 16 + 53$

The $24$th semiprime:

$69 = 3 \times 23$

The $27$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:

$3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $53$, $55$, $61$, $62$, $64$, $66$, $68$, $69$, $\ldots$

The $30$th odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime

$1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $\ldots$

Also see

• Number whose Square and Cube use all Digits Once

• Previous  ... Next: Squares Ending in 5 Occurrences of 2-Digit Pattern
• Previous  ... Next: Ulam Number
• Previous  ... Next: Semiprime Number
• Previous  ... Next: Odd Numbers Not Expressible as Sum of 4 Distinct Non-Zero Coprime Squares
• Previous  ... Next: 91 is Pseudoprime to 35 Bases less than 91

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $69$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $69$