OFFSET
1,5
FORMULA
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))).
EXAMPLE
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).
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Sep 15 2020
STATUS
approved