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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A002121 A279158 A273166

Adjacent sequences:  A300812 A300813 A300814 * A300816 A300817 A300818

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 13 2018

STATUS

approved

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Last modified October 16 20:09 EDT 2021. Contains 348044 sequences. (Running on oeis4.)