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

Author

Juri-Stepan Gerasimov, Jun 15 2014

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000005, A132881, A243865.

Programs

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 *)

PARI

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

Formula

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

Extensions

Corrected by Michel Marcus, Jun 27 2014