Problem 204
Generalised Hamming Numbers
A Hamming number is a positive number which has no prime factor larger than 5.
So the first few Hamming numbers are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15.
There are 1105 Hamming numbers not exceeding 108.
We will call a positive number a generalised Hamming number of type n, if it has no prime factor larger than n.
Hence the Hamming numbers are the generalised Hamming numbers of type 5.
How many generalised Hamming numbers of type 100 are there which don’t exceed 109?
广义汉明数
若一个正整数的所有质因数均不超过5，则被称为汉明数。
前几个汉明数分别是1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15。
在不超过108的正整数中，一共有1105个汉明数。
若一个正整数的所有质因数均不超过n，则被称为n型广义汉明数。
因此本来的汉明数就是5型广义汉明数。
在不超过109的正整数中，一共有多少个100型广义汉明数？