Almost prime
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In mathematics, a natural number n is called k-almost prime iff Ω(n) = k, where Ω(n) is the sum of the exponents in the prime decomposition of n:
- <math>\Omega(n) := \sum a_i \qquad\mbox{if}\qquad n = \prod p_i^{a_i}.<math>
A natural number is thus prime iff it is 1-almost prime, and semiprime iff it is 2-almost prime. The set of k-almost prime numbers is usually denoted by Pk. The first few k-almost prime numbers are:
k k-almost prime numbers OEIS sequence 1 2, 3, 5, 7, 11, 13, 17, 19, ... A000040 (http://www.research.att.com/projects/OEIS?Anum=A000040) 2 4, 6, 9, 10, 14, 15, 21, 22, ... A001358 (http://www.research.att.com/projects/OEIS?Anum=A001358) 3 8, 12, 18, 20, 27, 28, 30, ... A014612 (http://www.research.att.com/projects/OEIS?Anum=A014612) 4 16, 24, 36, 40, 54, 56, 60, ... A014613 (http://www.research.att.com/projects/OEIS?Anum=A014613) 5 32, 48, 72, 80, 108, 112, ... A014614 (http://www.research.att.com/projects/OEIS?Anum=A014614) 6 64, 96, 144, 160, 216, 224, ... A046306 (http://www.research.att.com/projects/OEIS?Anum=A046306) 7 128, 192, 288, 320, 432, 448, ... A046308 (http://www.research.att.com/projects/OEIS?Anum=A046308) 8 256, 384, 576, 640, 864, 896, ... A046310 (http://www.research.att.com/projects/OEIS?Anum=A046310) 9 512, 768, 1152, 1280, 1728, ... A046312 (http://www.research.att.com/projects/OEIS?Anum=A046312) 10 1024, 1536, 2304, 2560, ... A046314 (http://www.research.att.com/projects/OEIS?Anum=A046314) 11 2048, 3072, 4608, 5120, ... A069272 (http://www.research.att.com/projects/OEIS?Anum=A069272) 12 4096, 6144, 9216, 10240, ... A069273 (http://www.research.att.com/projects/OEIS?Anum=A069273) 13 8192, 12288, 18432, 20480, ... A069274 (http://www.research.att.com/projects/OEIS?Anum=A069274) 14 16384, 24576, 36864, 40960, ... A069275 (http://www.research.att.com/projects/OEIS?Anum=A069275) 15 32768, 49152, 73728, 81920, ... A069276 (http://www.research.att.com/projects/OEIS?Anum=A069276) 16 65536, 98304, 147456, ... A069277 (http://www.research.att.com/projects/OEIS?Anum=A069277) 17 131072, 196608, 294912, ... A069278 (http://www.research.att.com/projects/OEIS?Anum=A069278) 18 262144, 393216, 589824, ... A069279 (http://www.research.att.com/projects/OEIS?Anum=A069279) 19 524288, 786432, 1179648, ... A069280 (http://www.research.att.com/projects/OEIS?Anum=A069280) 20 1048576, 1572864, 2359296, ... A069281 (http://www.research.att.com/projects/OEIS?Anum=A069281) External links
- MathWorld: Almost prime (http://mathworld.wolfram.com/AlmostPrime.html)fr:Nombre presque premier