A243917 - OEIS

%I #29 May 27 2016 14:58:50

%S 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,

%T 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,

%U 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

%N Number of non-twin divisors of n.

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

%H Jens Kruse Andersen, <a href="/A243917/b243917.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

%t 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 *)

%t 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 *)

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

%Y Cf. A000005, A132881, A243865.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Jun 15 2014

%E Corrected by _Michel Marcus_, Jun 27 2014