38 (number)

38
Cardinalthirty-eight
Ordinal38th
(thirty-eighth)
Factorization$2 \cdot 19$
Divisors1, 2, 19, 38
Roman numeralXXXVIII
Binary1001102
Ternary11023
Quaternary2124
Octal468
Duodecimal3212
Vigesimal1I20
Base 361236

This article discusses the number thirty-eight. For the year 38 CE, see 38. For other uses of 38, see 38 (disambiguation)

38
Cardinalthirty-eight
Ordinal38th
(thirty-eighth)
Factorization$2 \cdot 19$
Divisors1, 2, 19, 38
Roman numeralXXXVIII
Binary1001102
Ternary11023
Quaternary2124
Octal468
Duodecimal3212
Vigesimal1I20
Base 361236

38 (thirty-eight) is the natural number following 37 and preceding 39.

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.[1]

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.[2]

In mythology

• The number 38 was especially prominent in Norse mythology. The number was said to represent unnatural bravery, characteristic of the legendary heroes of Norse sagas. Most legendary sagas were divided into 38 chapters, and the number often recurred throughout stories, with the heroes combating giants or other beasts in groups of 38. The number came to be adopted by the Hardrada clan, and was displayed on their crest in the form of 38 ravens set around 38 outward-facing arrows.[citation needed]
• The number was also significant in Egyptian mythology, as it was the characteristic number of Anubis, the jackal-headed god of death and mummification. Egyptian pharaohs were often buried with 38 statues of cat guardians, and their sarcophagi were adorned with 38 ankhs.

In other fields

Most people will see the number 38, but people with red-green color blindness might see 88 instead.

Thirty-eight is also:

Historical years

38 A.D., 38 B.C., 1938 A.D., 2038, etc.

References

1. ^ (sequence A005277 in OEIS)
2. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1.