A111861 a(n) is the number of integers k > 0 such that (n+k)/(n-k)^2 is an integer.

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

0,2

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

Robert Israel, Table of n, a(n) for n = 0..10000

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

Maple

g:=  proc(n) nops(select(t -> ((n+t)/(n-t)^2)::integer, {$1..floor(n+(1+sqrt(8*n+1))/2)} minus {n})) end proc:
map(g, [$0..105]); # Robert Israel, Oct 30 2024

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

Corrected by Robert Israel, Oct 30 2024

Status

approved