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殆素数 - Wikipedia

殆素数

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数学中,自然数n叫做k次殆素数当且仅当Ω(n) = k,这里Ω(n)是在n的素数分解过程中的指数和:

\Omega(n) := \sum a_i \qquad\mbox{if}\qquad n = \prod p_i^{a_i}

因此,一个自然数是素数当且仅当它是一次殆素数,一个自然数是半素数当且仅当它是二次殆素数。k次殆素数的集合通常表示成Pk。开始的几个k次殆素数是:

k k次殆素数 OEIS 数列
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

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