%I #9 Feb 01 2021 21:08:36

%S 0,0,0,0,2,1,8,5,13,13,32,14,50,40,51,50,98,61,128,85,128,142,200,114,

%T 220,217,241,219,338,221,392,309,390,415,449,337,578,538,575,478,722,

%U 540,800,677,720,832,968,680,1011,916,1053,1002,1250,1002,1247,1096,1346,1393,1568

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

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

%e a(7) = 8; There are 8 distinct positive integer pairs, (s,t), such that s < t < 7 where neither s, t, nor (s + t) divides n. They are (2,3), (2,4), (2,6), (3,5), (3,6), (4,5), (4,6) and (5,6).

%t Table[Sum[Sum[(Ceiling[n/(k + i)] - Floor[n/(k + i)]) (Ceiling[n/k] - Floor[n/k]) (Ceiling[n/i] - Floor[n/i]), {i, k - 1}], {k, n}], {n, 80}]

%Y Cf. A335567, A337273, A337588, A337679, A337680, A337681, A337682, A337683.

%K nonn,easy

%O 1,5

%A _Wesley Ivan Hurt_, Sep 15 2020