In Mathematics
38 is the 11th distinct semiprime and the 7th in the {2.q} family. It is the initial member of the third distinct semiprime pair (38, 39).
38 has an aliquot sum of 22 which is itself a distinct semiprime In fact 38 is the first number to be at the head of a chain of four distinct semiprimes in its 8 member aliquot sequence (38, 22, 14, 10, 8, 7, 1, 0). 38 is the 8th member of the 7-aliquot tree.
38! - 1 yields 523022617466601111760007224100074291199999999, which is the 16th factorial prime.
There is no answer to the equation φ(x) = 38, making 38 a nontotient.
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.
There are only two normal magic hexagons, order 1 (which is trivial) and order 3. The sum of each row of an order 3 magic hexagon is 38.
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