39 (number)

In mathematics

• 39 is the 12th distinct semiprime and the 4th in the (3.q) family. 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 number (39,17,1,0) to the Prime in the 17-aliquot tree.

• It is a perfect totient number.

• 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 (3 + 3 + 3). Given 39, the Mertens function returns 0.

• 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}.

• 39 is a Perrin number, coming after 17, 22, 29 (it is the sum of the first two mentioned).

• Since the greatest prime factor of 392 + 1 = 1522 is 761, which is more than 39 twice, 39 is a Størmer number.

• The F26A graph is a symmetric graph with 39 edges.

In other fields

Arts and entertainment

• Japanese wordplay and slang:
  • Through numeric substitution, 39 is the Internet chat slang term for "Thank you" when written with numbers: and .
  • 39 has also been associated with the virtual singer Hatsune Miku for the same reason: can also be read as , and can also be read as . Thus, if using the alternative readings, can also be read as .

History

• In Afghanistan, the number 39 is considered unlucky, due to the belief that it is associated with pimps.

References

References

1. {{Cite OEIS
2. {{Cite OEIS
3. "Sloane's A082897 : Perfect totient numbers". OEIS Foundation.
4. "Sloane's A028442 : Numbers n such that Mertens' function is zero". OEIS Foundation.
5. "Sloane's A001608 : Perrin sequence". OEIS Foundation.
6. "Sloane's A005528 : Størmer numbers". OEIS Foundation.
7. (2 November 2017). "Here's Why the Number "39" Means "Thank You" in Japan". Reader's Digest.
8. "Definition of 三".
9. "Definition of 九".
10. "3/9 Marks Happy "Miku" & "Zaku" Day In Japan, Fan Artists Mark The Occasion". Crunchyroll.
11. "What's up with Miku and 39?".
12. (17 November 2011). "Loya jirga: Afghan elders reject 'pimp's number 39'". BBC News.