A145264 a(n) is the positive integer such that Sum_{k>=0} floor(n/(a(n)+k)) = n, or 0 if there is no such positive integer.

1, 0, 0, 2, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 5, 0, 0, 6, 6, 0, 0, 7, 7, 0, 0, 8, 0, 0, 0, 0, 0, 0, 10, 0, 0, 11, 11, 0, 0, 12, 12, 0, 0, 13, 0, 0, 0, 0, 0, 0, 15, 0, 0, 16, 16, 0, 0, 17, 17, 0, 0, 18, 0, 0, 0, 0, 0, 0, 20, 0, 0, 21, 21, 0, 0, 22, 22, 0, 0, 23, 0, 0, 0, 0, 0, 0, 25, 0, 0, 26, 26, 0, 0, 27, 27

Offset

1,4

Links

Table of n, a(n) for n=1..95.

Example

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 at which to start the sequence of denominators so that the sum is 6.

Maple

A145264 := proc(n) local a, k; for a from 1 to n do if add( floor(n/(a+k)), k=0..n-a) = n then RETURN(a) ; fi; od: RETURN(0) ; end: for n from 1 to 120 do printf("%d, ", A145264(n)) ; od: # R. J. Mathar, Oct 07 2008

Crossrefs

Cf. A145265, A145266.

Sequence in context: A354643 A282516 A158092 * A300333 A357019 A352562

Adjacent sequences: A145261 A145262 A145263 * A145265 A145266 A145267

Keyword

nonn

Author

Leroy Quet, Oct 05 2008

Extensions

More terms from R. J. Mathar, Oct 07 2008

Status

approved