Almost prime
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In mathematics, a natural number n is called k-almost prime iff it can be written as a product of exactly k prime factors. More formally, a number is 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 2 4, 6, 9, 10, 14, 15, 21, 22, ... A001358 3 8, 12, 18, 20, 27, 28, 30, ... A014612 4 16, 24, 36, 40, 54, 56, 60, ... A014613 5 32, 48, 72, 80, 108, 112, ... A014614 6 64, 96, 144, 160, 216, 224, ... A046306 7 128, 192, 288, 320, 432, 448, ... A046308 8 256, 384, 576, 640, 864, 896, ... A046310 9 512, 768, 1152, 1280, 1728, ... A046312 10 1024, 1536, 2304, 2560, ... A046314 11 2048, 3072, 4608, 5120, ... A069272 12 4096, 6144, 9216, 10240, ... A069273 13 8192, 12288, 18432, 20480, ... A069274 14 16384, 24576, 36864, 40960, ... A069275 15 32768, 49152, 73728, 81920, ... A069276 16 65536, 98304, 147456, ... A069277 17 131072, 196608, 294912, ... A069278 18 262144, 393216, 589824, ... A069279 19 524288, 786432, 1179648, ... A069280 20 1048576, 1572864, 2359296, ... A069281 [edit]External links