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Almost prime

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:

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:

kk-almost prime numbersSloane sequence
12, 3, 5, 7, 11, 13, 17, 19, ...A000040
24, 6, 9, 10, 14, 15, 21, 22, ...A001358
38, 12, 18, 20, 27, 28, 30, ...A014612
416, 24, 36, 40, 54, 56, 60, ...A014613
532, 48, 72, 80, 108, 112, ...A014614
664, 96, 144, 160, 216, 224, ...A046306
7128, 192, 288, 320, 432, 448, ...A046308
8256, 384, 576, 640, 864, 896, ...A046310
9512, 768, 1152, 1280, 1728, ...A046312
101024, 1536, 2304, 2560, ...A046314
112048, 3072, 4608, 5120, ...A069272
124096, 6144, 9216, 10240, ...A069273
138192, 12288, 18432, 20480, ...A069274
1416384, 24576, 36864, 40960, ...A069275
1532768, 49152, 73728, 81920, ...A069276
1665536, 98304, 147456, ...A069277
17131072, 196608, 294912, ...A069278
18262144, 393216, 589824, ...A069279
19524288, 786432, 1179648, ...A069280
201048576, 1572864, 2359296, ...A069281

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