A111150 a(n) is the number of integers of the form (n+k)/|(n-k)| for k>0.

2, 4, 6, 6, 6, 10, 6, 8, 10, 10, 6, 14, 6, 10, 14, 10, 6, 16, 6, 14, 14, 10, 6, 18, 10, 10, 14, 14, 6, 22, 6, 12, 14, 10, 14, 22, 6, 10, 14, 18, 6, 22, 6, 14, 22, 10, 6, 22, 10, 16, 14, 14, 6, 22, 14, 18, 14, 10, 6, 30, 6, 10, 22, 14, 14, 22, 6, 14, 14, 22, 6, 28, 6, 10, 22, 14, 14, 22

Offset

1,1

Comments

a(n) <= 2^(n-1) and a(p)=6 for odd primes. - Robert G. Wilson v

Links

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

Formula

a(n) = 2*tau(2n) - 2, tau = A000005. - Ivan Neretin, Sep 07 2017

Example

For n=7 we have integer value for the form when k={5; 6; 8; 9; 14; 21} and (7+k)/|(7-k)| = {6, 13, 15, 8, 3, 2}. Thus a(7) = 6.

Mathematica

f[n_] := Length[ Select[(n + #)/Abs[n - # ] & /@ Delete[ Range[ Floor[5n/3]], n], IntegerQ[ # ] &]] + 2; Array[f, 78] (* Robert G. Wilson v *)
Table[2 DivisorSigma[0, 2 n] - 2, {n, 78}] (* Ivan Neretin, Sep 07 2017 *)

Crossrefs

Cf. A000005.

Sequence in context: A207540 A050825 A174342 * A166983 A361689 A078611

Adjacent sequences: A111147 A111148 A111149 * A111151 A111152 A111153

Keyword

easy,nonn

Author

Paolo P. Lava & Giorgio Balzarotti, Oct 19 2005

Extensions

Edited and extended by Robert G. Wilson v, Oct 19 2005

Status

approved