39

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

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 (3^1 + 3^2 + 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 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

The thirteenth Perrin number is 39, which comes 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 obviously more than 39 twice, 39 is a Størmer number.

The F26A graph is a symmetric graph with 39 edges.

See wikipedia on 39