A111164 Number of distinct integers of the form (n+k)/|(n-k)| for k > 0.

2, 3, 5, 5, 6, 7, 6, 7, 9, 9, 6, 10, 6, 9, 12, 9, 6, 13, 6, 12, 13, 9, 6, 14, 10, 9, 13, 13, 6, 17, 6, 11, 13, 9, 13, 18, 6, 9, 13, 16, 6, 18, 6, 13, 20, 9, 6, 18, 10, 15, 13, 13, 6, 19, 14, 16, 13, 9, 6, 23, 6, 9, 20, 13, 14, 19, 6, 13, 13, 20, 6, 23, 6, 9, 20, 13, 14, 19, 6, 20, 17, 9, 6

Offset

1,1

Comments

Integers of the form (n+k)/|(n-k)| for integer k are exactly the numbers d-1 and d+1 where d runs through the divisors of 2n. Of those, 0 and 1 do not count because they correspond to nonpositive k. - Ivan Neretin, Sep 07 2017

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

For n=14 we have integer values of this form when k={7; 10; 12; 13; 15; 16; 18; 19; 21; 28; 42} and (14+k)/|(14-k)| = {3, 6, 13, 27, 29, 15, 8, 5, 3, 2}. Thus a(14) = 9 because 3 is present twice.

Mathematica

f[n_] := Length[ Union[ Select[(n + #)/Abs[n - # ] & /@ Delete[ Range[ Floor[3n]], n], IntegerQ[ # ] &]]]; Array[f, 83] (* Robert G. Wilson v, Oct 31 2005 *)
Table[d = Divisors[2 n]; Length@Union[Drop[d - 1, 2], d + 1], {n, 83}] (* Ivan Neretin, Sep 07 2017 *)

Crossrefs

Cf. A111150.

Sequence in context: A169787 A165959 A347784 * A255347 A029910 A063677

Adjacent sequences: A111161 A111162 A111163 * A111165 A111166 A111167

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 21 2005

Extensions

Corrected and extended by Robert G. Wilson v, Oct 31 2005

Status

approved