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(n/(i+k)) + floor(n/(i+k))).
EXAMPLE
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.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Sep 15 2020
STATUS
approved