39 (number)

 ← 38 39 40 →
Cardinal thirty-nine
Ordinal 39th
(thirty-ninth)
Factorization 3 × 13
Divisors 1, 3, 13, 39
Roman numeral XXXIX
Binary 1001112
Ternary 11103
Quaternary 2134
Quinary 1245
Senary 1036
Octal 478
Duodecimal 3312
Vigesimal 1J20
Base 36 1336

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

In mathematics

The F26A graph has 39 edges, all equivalent.

Thirty-nine is the sum of 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.[1]

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 the 12th distinct semiprime and the 4th in the {3.q} family. It is the last member of the third distinct biprime pair (38,39).

39 has an aliquot sum of 17 which is itself a prime. 39 is the 4th member of the 17-aliquot tree. It is a perfect totient number.[2]

The thirteenth Perrin number is 39, which comes after 17, 22, 29 (it is the sum of the first two mentioned).[3]

Since the greatest prime factor of 392 + 1 = 1522 is 761, which is obviously more than 39 twice, 39 is a Størmer number.[4]

The F26A graph is a symmetric graph with 39 edges.

Astronomy

In other fields

Arts and entertainment
History
• The number of signers to the United States Constitution, out of 55 members of the Philadelphia Convention delegates
• The traditional number of times citizens of Ancient Rome hit their slaves when beating them, referred to as "Forty save one"
• The duration, in nanoseconds, of the nuclear reaction in the largest nuclear explosion ever performed (Tsar bomb)
• The number of Scud missiles which Iraq fired at Israel during the Gulf War in 1991
Other

References

1. "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
2. "Sloane's A082897 : Perfect totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
3. "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
4. "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
5. "Loya jirga: Afghan elders reject 'pimp's number 39'". BBC News. 17 November 2011. Retrieved 3 May 2012.
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