38

38 = 2 x 19.

38 is the largest even number that cannot be written as the sum of two odd composite numbers.

38 is the magic constant in the only possible magic hexagon (which uses all the integers up to and including 19).

38 is the number of integer partitions of 17 into distinct parts.

The snub cube is an Archimedean solid with 38 faces.

Source: Number Gossip