A243917 Number of non-twin divisors of n.

1, 2, 0, 1, 2, 2, 2, 2, 1, 4, 2, 1, 2, 4, 1, 3, 2, 4, 2, 4, 2, 4, 2, 2, 3, 4, 2, 4, 2, 5, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 6, 2, 4, 3, 4, 2, 4, 3, 6, 2, 4, 2, 6, 4, 6, 2, 4, 2, 4, 2, 4, 2, 5, 4, 6, 2, 4, 2, 6, 2, 6, 2, 4, 3, 4, 4, 6, 2, 6, 3, 4, 2, 5, 4, 4, 2, 6, 2, 9, 4, 4, 2, 4, 4, 6

Offset

1,2

Comments

A divisor k of n is non-twin if neither the positive values of k - 2 nor k + 2 divide n.

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000005(n) - A243865(n).

Example

The positive divisors of 12 are: 1, 2, 3, 4, 6, 12. Of these, 1 and 3 are twin divisors, 2, 4 and 6 are also twin divisors. The unique non-twin divisor is therefore 12. So a(12) = the number of these divisors, which is 1.

Mathematica

a243917[n_Integer] := Length[Select[Divisors[n], If[And[# <= 2 || Divisible[n, # - 2] == False, Divisible[n, # + 2] == False], True, False] &]]; a243917 /@ Range[120] (* Michael De Vlieger, Aug 17 2014 *)
nntd[n_]:=Module[{d=Select[Divisors[n], #>2&], t}, t=Count[d, _?(!Divisible[ n, #-2] && !Divisible[ n, #+2]&)]; If[!Divisible[ n, 3], t++]; If[ Divisible[ n, 2] && !Divisible[n, 4], t++]; t]; Array[nntd, 100] (* Harvey P. Dale, May 27 2016 *)

Prog

(PARI) a(n) = sumdiv(n, d, (((d<=2) || (n % (d-2))) && (n % (d+2)))); \\ Michel Marcus, Jun 25 2014

Crossrefs

Cf. A000005, A132881, A243865.

Sequence in context: A028832 A260411 A199331 * A254212 A033773 A029275

Adjacent sequences: A243914 A243915 A243916 * A243918 A243919 A243920

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 15 2014

Extensions

Corrected by Michel Marcus, Jun 27 2014

Status

approved