specifically, the 11th discrete
Semiprime,[1] it being the 7th of the form (2.q).
the first member of the third cluster of two discrete semiprimes 38,
39 the next such cluster is
57,
58.
with an
aliquot sum of
22 in an
aliquot sequence of five composite numbers (38,
22,
14,
10,
8,
7,
1,0) to the Prime in the
7-aliquot tree. 34 is the first
semiprime within a chain of 4 semiprimes in its
aliquot sequence (38,
22,
14,
10). The next semiprime with a four semiprime chain is
166.
38
! − 1 yields 523022617466601111760007224100074291199999999 which is the 16th
factorial prime.[2]
There is no answer to the equation
φ(x) = 38, making 38 a
nontotient.[3]
38 is the sum of the
squares of the first three
primes.
37 and 38 are the first pair of consecutive positive integers not divisible by any of their digits.
38 is the largest even number which cannot be written as the sum of two odd
composite numbers.
The sum of each row of the only non-trivial (order 3)
magic hexagon is 38.[4]