← 38 39 40 →
Cardinalthirty-nine
Ordinal39th
(thirty-ninth)
Factorization3 × 13
Divisors1, 3, 13, 39
Greek numeralΛΘ´
Roman numeralXXXIX
Binary1001112
Ternary11103
Senary1036
Octal478
Duodecimal3312

39 (thirty-nine) is the natural number following 38 and preceding 40.

## In mathematics

• 39 is the 12th distinct semiprime[1] and the 4th in the (3.q) family.[2] It is the last member of the third distinct semiprime pair (38,39).
• 39 has an aliquot sum of 17, which is a prime. 39 is the 4th member of the 17-aliquot tree within an aliquot sequence of one composite numbers (39,17,1,0) to the Prime in the 17-aliquot tree.
• It is a perfect totient number.[3] *39 is the sum of five consecutive primes (3 + 5 + 7 + 11 + 13) and also is the product of the first and the last of those consecutive primes. Among small semiprimes only three other integers (10, 155, and 371) share this attribute. 39 also is the sum of the first three powers of 3 (31 + 32 + 33). Given 39, the Mertens function returns 0.[4]
• 39 is the smallest natural number which has three partitions into three parts which all give the same product when multiplied: {25, 8, 6}, {24, 10, 5}, {20, 15, 4}.

## References

1. ^ Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ Sloane, N. J. A. (ed.). "Sequence A001748". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ "Sloane's A082897 : Perfect totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
4. ^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
5. ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
6. ^ "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
7. ^ Specktor, Brandon (2 November 2017). "Here's Why the Number "39" Means "Thank You" in Japan". Reader's Digest. Retrieved 23 March 2021.
8. ^ "Loya jirga: Afghan elders reject 'pimp's number 39'". BBC News. 17 November 2011. Retrieved 3 May 2012.