单选题Let Ω p be defined as p2/3-p for all positive integers, p. If Ωn = s, and s is a positive integer, which of the following is a possible value for s?A1B3C5D6E8
单选题
Let Ω p be defined as p2/3-p for all positive integers, p. If Ωn = s, and s is a positive integer, which of the following is a possible value for s?
A
1
B
3
C
5
D
6
E
8
参考解析
解析：
根据题干Ωn =n2 /3-n=s. n为正整数，且s为正整数；根据函数可知只有当n是3的倍数时，s才能为整数，否则如果n2 /3不是整数，s也不是整数。现在可以从符合条件的n的最小值3代入到函数中。当n=3时，n2 /3-n =32 /3-3 = 3-3 = 0 = s；当n=6时，n2 /3-n = 62 /3-6 = 12-6 = 6 = s。所以故选D。
根据题干Ωn =n2 /3-n=s. n为正整数，且s为正整数；根据函数可知只有当n是3的倍数时，s才能为整数，否则如果n2 /3不是整数，s也不是整数。现在可以从符合条件的n的最小值3代入到函数中。当n=3时，n2 /3-n =32 /3-3 = 3-3 = 0 = s；当n=6时，n2 /3-n = 62 /3-6 = 12-6 = 6 = s。所以故选D。
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