**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.

Read more about this topic: 38 (number)

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### Famous quotes containing the word mathematics:

“... though *mathematics* may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.”

—Amelia E. Barr (1831–1919)

“*Mathematics* alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In *mathematics* we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of *mathematics* is in relation to our intelligence.”

—Simone Weil (1909–1943)