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奢侈数(英语:Extravagant number)也称为浪费数(英语:Wasteful number),是指一正整数质因数分解(包括指数)的总位数大于整数本身的位数[1]。例如在十进制中,4 = 22,6 = 2×3,8 = 23,9 = 32,质因数分解的总位数都比整数位数多,因此都是奢侈数。

前几个奢侈数为:

4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100(OEIS数列A046760

任何进制下都可以定义奢侈数,而且不论在哪一种进制,都存在无限多个奢侈数[1]

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