A337682 - OEIS

%I #9 Feb 01 2021 20:52:54

%S 0,0,0,0,0,0,1,1,0,1,1,0,3,3,2,3,4,2,5,3,5,6,6,3,7,8,6,7,9,5,12,10,11,

%T 12,11,7,15,15,14,10,17,12,19,18,14,21,21,13,22,20,22,22,23,18,23,19,

%U 25,26,26,14,31,31,26,28,31,29,34,33,33,29,36,21,39,39,34,39,39,38

%N Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s nor t divides n, and (s + t) | (s * t).

%F a(n) = Sum_{k=1..n} Sum_{i=1..k-1} (ceiling(n/k) - floor(n/k)) * (ceiling(n/i) - floor(n/i)) * (1 - ceiling((i*k)/(i+k)) + floor((i*k)/(i+k))).

%e a(13) = 3; There are 3 distinct positive integer pairs, (s,t), such that s < t < 13 where neither s nor t divides 13, and where (s + t) | (s * t). They are (3,6), (4,12) and (6,12).

%t Table[Sum[Sum[(1 - Ceiling[(i*k)/(k + i)] + Floor[(i*k)/(k + i)]) (Ceiling[n/k] - Floor[n/k]) (Ceiling[n/i] - Floor[n/i]), {i, k - 1}], {k, n}], {n, 100}]

%Y Cf. A335567, A337273, A337588, A337679, A337680, A337681, A337683, A337684.

%K nonn,easy

%O 1,13

%A _Wesley Ivan Hurt_, Sep 15 2020