A111861 a(n) is the number of integers of the form (n+k)/(n-k)^2 for k>0.

1, 2, 2, 5, 2, 4, 4, 4, 2, 4, 4, 4, 3, 4, 3, 7, 2, 4, 3, 4, 2, 7, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 2, 6, 3, 5, 4, 4, 3, 6, 3, 4, 4, 4, 2, 6, 3, 4, 3, 4, 3, 6, 2, 4, 3, 6, 2, 6, 3, 4, 5, 4, 3, 4, 2, 5, 6, 4, 3, 6, 4, 4, 2, 4, 3, 6, 2, 5, 6, 4, 2, 4, 3, 4, 3, 5, 3, 6, 2, 4, 4, 6, 3, 6, 3, 5, 3, 4, 3, 4, 3, 4, 4, 4, 2

Offset

1,2

Comments

First occurrence of n [0,500] is at a(k): 0,1,12,5,3,33,15,210,105, ..., . - Robert G. Wilson v, Nov 23 2005

Links

Table of n, a(n) for n=1..105.

Example

For n=14 we have integer value for the form when k={13; 15; 18} and (14+k)/(14-k)^2 = {27, 29, 2}. Thus a(14) = 3

Mathematica

f[n_] := Length[Select[(n + #)/(n - #)^2 & /@ Range[n^2 + 3], IntegerQ[ # ] &]]; Array[f, 105] (* Robert G. Wilson v *)

Crossrefs

Cf. A111150, A111164.

Sequence in context: A351346 A061034 A245635 * A004543 A153078 A245565

Adjacent sequences: A111858 A111859 A111860 * A111862 A111863 A111864

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 22 2005

Extensions

Corrected and extended by Robert G. Wilson v, Nov 23 2005

Status

approved