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In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. The smallest sphenic number is 30 = 2 × 3 × 5, the product of the smallest three primes. Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic. All sphenic numbers have exactly eight divisors. If we express the sphenic number as , where ''p'', ''q'', and ''r'' are distinct primes, then the set of divisors of ''n'' will be: : All sphenic numbers are by definition squarefree, because the prime factors must be distinct. The Möbius function of any sphenic number is −1. The cyclotomic polynomials , taken over all sphenic numbers ''n'', may contain arbitrarily large coefficients〔Emma Lehmer, "On the magnitude of the coefficients of the cyclotomic polynomial", ''Bulletin of the American Mathematical Society'' 42 (1936), no. 6, pp. 389–392.().〕 (for ''n'' a product of two primes the coefficients are or 0). The first few sphenic numbers are: 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, ... the largest known sphenic number is (257,885,161 − 1) × (243,112,609 − 1) × (242,643,801 − 1), i.e., the product of the three largest known primes. ==Consecutive sphenic numbers== The first case of two consecutive sphenic integers is 230 = 2×5×23 and 231 = 3×7×11. The first case of three is 1309 = 7×11×17, 1310 = 2×5×131, and 1311 = 3×19×23. There is no case of more than three, because every fourth consecutive positive integer is divisible by 4 = 2×2 and therefore not squarefree. The numbers 2013 (3×11×61), 2014 (2×19×53), and 2015 (5×13×31) are all sphenic. The next three consecutive sphenic years will be 2665 (5×13×41), 2666 (2×31×43) and 2667 (3×7×127) . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sphenic number」の詳細全文を読む スポンサード リンク
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