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

10,3

Links

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

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

Example

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]

Crossrefs

Cf. A003165.

Sequence in context: A262138 A308212 A181346 * A358933 A002121 A279158

Adjacent sequences: A300812 A300813 A300814 * A300816 A300817 A300818

Keyword

nonn

Author

Seiichi Manyama, Mar 13 2018

Status

approved