|
%I #9 Feb 01 2021 20:47:56
%S 0,0,0,0,3,1,8,3,9,9,18,6,26,22,24,22,39,23,47,31,48,54,63,30,71,71,
%T 71,64,90,60,104,82,103,109,111,74,134,130,132,103,153,121,167,149,
%U 151,177,186,122,197,181,202,194,220,180,224,194,238,244,253,167,276,272,258,253
%N Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s nor t divides n, and (t - s) | (t * s).
%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((k*i)/(k-i)) + floor((k*i)/(k-i))).
%e a(7) = 8; There are 8 distinct positive integer pairs, (s,t), such that s < t < 7, where neither s nor t divides 7 and (t - s) | (t * s). They are (2,3), (2,4), (2,6), (3,4), (3,6), (4,5), (4,6) and (5,6).
%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, A337682, A337683, A337684.
%K nonn,easy
%O 1,5
%A _Wesley Ivan Hurt_, Sep 15 2020
|
