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%I #9 Feb 01 2021 20:42:36
%S 0,0,0,0,1,0,2,1,2,2,4,1,5,5,4,5,7,5,8,6,8,11,10,6,11,14,12,12,13,10,
%T 14,16,16,20,16,14,17,23,20,18,19,21,20,26,21,29,22,23,24,30,28,33,25,
%U 33,28,32,32,38,28,28,29,41,34,42,34,44,32,47,40,43,34,41,35,50,44,54
%N Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s nor t divides n, and (s + t) | 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)) * (1 - ceiling(n/(i+k)) + floor(n/(i+k))).
%e a(7) = 2; There are 5 positive integers less than 7 that do not divide 7, {2,3,4,5,6}. Of these numbers, there are two pairs, (s,t), such that s < t < 7 where (s + t) | 7. They are (2,5) and (3,4). So a(7) = 2.
%t Table[Sum[Sum[(1 - Ceiling[n/(i + k)] + Floor[n/(i + k)]) (Ceiling[n/k] - Floor[n/k]) (Ceiling[n/i] - Floor[n/i]), {i, k - 1}], {k, n}], {n, 80}]
%Y Cf. A335567, A337273, A337588, A337680, A337681, A337682, A337683, A337684.
%K nonn,easy
%O 1,7
%A _Wesley Ivan Hurt_, Sep 15 2020