A300815 Number of 3 division {a, b, c} (a < b < c) of n where b isn't a multiple of a, c isn't a multiple of a and c isn't a multiple of b.

1, 0, 2, 0, 2, 2, 4, 2, 7, 3, 9, 8, 10, 7, 17, 11, 16, 16, 23, 17, 32, 21, 31, 30, 36, 36, 52, 36, 47, 49, 63, 50, 73, 56, 75, 77, 80, 74, 105, 87, 105, 101, 116, 102, 133, 123, 143, 136, 144, 137, 185, 148, 170, 180, 194, 187, 218, 191, 223, 219, 247, 224, 278, 237, 263, 276, 292, 283, 321, 292, 344, 326, 340, 329, 399, 361

Offset: 10

Author

Seiichi Manyama, Mar 13 2018

Keywords

• nonn

Examples

			n  |
------------------------------------------------------------------------------------
10 | [2, 3, 5]
12 | [2, 3, 7],  [3, 4, 5]
14 | [2, 5, 7],  [3, 4, 7]
15 | [3, 5, 7],  [4, 5, 6]
16 | [2, 3, 11], [2, 5, 9],  [3, 5, 8], [4, 5, 7]
17 | [3, 4, 10], [4, 6, 7]
18 | [2, 3, 13], [2, 5, 11], [2, 7, 9], [3, 4, 11], [3, 7, 8], [4, 5, 9], [5, 6, 7]
19 | [3, 5, 11], [4, 6, 9],  [5, 6, 8]
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 10..1000

Crossrefs

Cf. A003165.

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} c(i/j) * c((n-i-j)/i) * c((n-i-j)/j), where c(n) = ceiling(n) - floor(n). - Wesley Ivan Hurt, Apr 13 2021