Question 269002
It seems to me that you count 1, 2 and then primes greater than 5, and multiples of primes. Here is the list that I have:
1,  2, 
7, 14, 49, 77, 91, 98, 119, . . . .  . .. . . . . . .. [22 options] 
11, 22, 121, 143, 154,  . . .  . . .  . . . . . . . . [12 options
13, 26, 169, 182, 221, 247, 286, 299, 338 [9 options]
17, 34, 289, 323 . . . . . . . . . . . . . . . . . . . . .[4 options]
19, 38, 23, 46, 29, 58, 31, 62, 37, 74
41, 82, 43, 86, 47, 94, 53, 106, 59, 118,
61, 122, 67, 134, 71, 142, 73, 146, 77, 154, 
79, 158, 83, 166, 89, 178, 91, 182, 97, 194,
101, 202, 103, 206, 107, 214, 109, 218, 113, 226,
127, 254, 131, 262, 137, 274, 139, 278, 149, 298,
151, 302, 157, 314, 163, 326, 167, 334, 173, 346,
179, 358,
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181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 
239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 
293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 
359
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so our total appears to be: 2 + 22 + 12 + 9 + 4 + 72 + 31 = 152 good options
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On a personal note I didn't like this question. It could have been set up better using a smaller number such as 100 roses.