Smallest Consecutive Even Nontotients

Theorem

The smallest pair of consecutive even nontotients is $74$ and $76$.

Proof

From the sequence of nontotients:

The sequence of nontotients begins:

$14, 26, 34, 38, 50, 62, 68, 74, 76, 86, 90, 94, 98, 114, 118, 122, 124, 134, 142, 146, 152, 154, \ldots$

Hence, by inspection, it can be seen that $74$ and $76$ are the smallest such pair.

$\blacksquare$

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $74$