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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.
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}.
39 is a Perrin number, coming after 17, 22, 29 (it is the sum of the first two mentioned).[5]
Since the greatest prime factor of 392 + 1 = 1522 is 761, which is more than 39 twice, 39 is a Størmer number.[6]
Internet chat slang for "Thank You" when written with numbers: 3 (三, san) and 9 (九, kyū).[7]
39 has been associated with the virtual singer Hatsune Miku because the written form of "Mi" (ミ) and the phonic pronunciation of "ku" (ク) have similarity to the numbers 3 (三, san) and 9 (九, kyū).[8]
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 Bomba)