OFFSET
1,2
COMMENTS
Defining a(n,b) as the number of equations of the set E_{n,b} which admit at least one nonnegative integer solution, it's possible to prove the existence of b_0 such that for all b > b_0, a(n,b) = a(n) whose value does not depend on b anymore.
a(n) is the number of positive integers k such that k(k+1) <= n or k divides n or k+1 divides n.
FORMULA
EXAMPLE
a(11) = 4 since for all b >= 29 the number of equations of the set E_{11,b} which admit at least one nonnegative integer solution is exactly equal to 4.
a(4) = 4 since for all b >= 1 the number of equations of the set E_{11,b} which admit at least one nonnegative integer solution is exactly equal to 4.
MATHEMATICA
Table[Ceiling[Sqrt[n] - 3/2] + Length[Divisors[n]], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Luca Onnis, Oct 10 2022
STATUS
approved