cp's OEIS Frontend

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.

%I A300815 #17 Apr 22 2021 21:52:38
%S A300815 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,
%T A300815 36,47,49,63,50,73,56,75,77,80,74,105,87,105,101,116,102,133,123,143,
%U A300815 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
%N 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.
%H A300815 Seiichi Manyama, <a href="/A300815/b300815.txt">Table of n, a(n) for n = 10..1000</a>
%F A300815 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
%e A300815 n  |
%e A300815 ------------------------------------------------------------------------------------
%e A300815 10 | [2, 3, 5]
%e A300815 12 | [2, 3, 7],  [3, 4, 5]
%e A300815 14 | [2, 5, 7],  [3, 4, 7]
%e A300815 15 | [3, 5, 7],  [4, 5, 6]
%e A300815 16 | [2, 3, 11], [2, 5, 9],  [3, 5, 8], [4, 5, 7]
%e A300815 17 | [3, 4, 10], [4, 6, 7]
%e A300815 18 | [2, 3, 13], [2, 5, 11], [2, 7, 9], [3, 4, 11], [3, 7, 8], [4, 5, 9], [5, 6, 7]
%e A300815 19 | [3, 5, 11], [4, 6, 9],  [5, 6, 8]
%Y A300815 Cf. A003165.
%K A300815 nonn
%O A300815 10,3
%A A300815 _Seiichi Manyama_, Mar 13 2018