OFFSET
1,7
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) + floor(k/i)).
EXAMPLE
a(11) = 8; There are 9 positive integers less than 11 that do not divide 11, {2,3,4,5,6,7,8,9,10}. Of these, there are 8 ordered pairs, (s,t), where s < t < 11 and s | t. They are (2,4), (2,6), (2,8), (2,10), (3,6), (3,9), (4,8) and (5,10).
MATHEMATICA
Table[Sum[Sum[(1 - Ceiling[k/i] + Floor[k/i]) (Ceiling[n/k] - Floor[n/k])(Ceiling[n/i] - Floor[n/i]), {i, k - 1}], {k, n}], {n, 80}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Sep 15 2020
STATUS
approved