68

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Number

$68$ (sixty-eight) is:

$2^2 \times 17$

The $7$th nontotient after $14$, $26$, $34$, $38$, $50$, $62$:

$\nexists m \in \Z_{>0}: \map \phi m = 68$

where $\map \phi m$ denotes the Euler $\phi$ function

The $12$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $28$, $31$, $32$, $44$, $49$:

$68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$

The $26$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:

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

The largest positive even integer that cannot be expressed as the sum of $2$ odd positive composite integers in at least $2$ different ways.

Also see

• Positive Even Integers as Sum of 2 Composite Odd Integers in 2 Ways

• Previous  ... Next: Happy Number
• Previous  ... Next: Nontotient
• Previous  ... Next: 91 is Pseudoprime to 35 Bases less than 91

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $68$