A337683 - OEIS

%I #9 Feb 01 2021 20:54:46

%S 0,0,0,0,0,0,2,1,1,1,2,0,4,3,3,4,6,2,8,5,8,9,10,3,11,11,9,10,14,7,18,

%T 14,16,17,17,9,22,21,20,13,24,16,28,25,21,31,32,19,33,28,32,31,34,25,

%U 34,28,36,37,38,17,44,43,37,40,44,40,50,47,48,39,52,28,56,55,48,55

%N Number of distinct positive integer pairs, (s,t), with s < t < n such that neither s nor t divides n and the harmonic mean of s and t is an integer.

%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(2*(k*i)/(k+i)) + floor(2*(k*i)/(k+i))).

%e a(7) = 2; There are 2 distinct positive integer pairs, (s,t), with s < t < 7 such that neither s nor t divides 7 and the harmonic mean of s and t is an integer. They are (2,6) and (3,6).

%t Table[Sum[Sum[(1 - Ceiling[2 (i*k)/(k + i)] + Floor[2 (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, A337682, A337684.

%K nonn,easy

%O 1,7

%A _Wesley Ivan Hurt_, Sep 15 2020