# 38 (number)

This article is about the number. For the year 38 CE, see 38. For other uses of 38, see 38 (disambiguation).
 ← 37 38 39 →
Cardinal thirty-eight
Ordinal 38th
(thirty-eighth)
Factorization 2 × 19
Divisors 1, 2, 19, 38
Roman numeral XXXVIII
Binary 1001102
Ternary 11023
Quaternary 2124
Quinary 1235
Senary 1026
Octal 468
Duodecimal 3212
Hexadecimal 2616
Vigesimal 1I20
Base 36 1236

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.

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.

## 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:

## References

1. "Sloane's A002982 : Numbers n such that n! - 1 is prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
2. (sequence A005277 in the OEIS)
3. Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1.
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