Math Forum / Mathematics / General Topics / October 2008

I just submitted this sequence to the Encyclopedia of Integer
Sequences.
(http://www.research.att.com/~njas/sequences/ )

%S A145264 1,0,0,2,2,0,0,3,0,0,0,0,0,0,5,0
%N A145264 a(n) is the positive integer such that sum{k>=0} floor(n/
(a(n)+k)) = n. a(n) = 0 if there is no such positive integer.
%e A145264 For n = 8: floor(8/3) + floor(8/4) + floor(8/5) +
floor(8/6) + floor(8/7) + floor(8/8) = 2 + 2 + 1 + 1 + 1 + 1 = 8. So
a(8) = 3. For n = 6: floor(6/2) + floor(6/3) + floor(6/4) + floor(6/5)
+ floor(6/6) = 3 + 2 + 1 + 1 + 1 = 8, which is > 6. But floor(6/3) +
floor(6/4) + floor(6/5) + floor(6/6) = 2 + 1 + 1 + 1 = 5, which is <
6. So, a(6) = 0, because there is no integer to start the sequence of
denominators at so that the sum is 6.
%Y A145264 A145265,A145266
%K A145264 more,nonn

As the description says:
a(n) is the positive integer such that sum{k>=0} floor(n/(a(n)+k)) =
n. a(n) = 0 if there is no such positive integer.

(See examples above in the %e-line.)

What I wonder is, is there an easy way to determine which terms are
positive and which are 0?
(For instance: Maybe a(n) >= 1 if n is congruent to this, that, and
something else (mod x), for some x.)

(Note: Sequence A145265 is the list of n's where a(n) is positive. And
A145266 is the list of n's where a(n) = 0.)

Thanks,
Leroy Quet