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A243932 Positive integers with the same number of twin divisors as non-twin divisors.

%I A243932 #22 Jul 16 2014 06:30:04
%S A243932 6,8,21,27,33,35,39,40,45,51,57,69,72,75,87,93,96,105,111,123,129,141,
%T A243932 143,159,168,177,183,189,201,213,219,237,249,252,264,267,291,297,303,
%U A243932 309,312,321,323,327,339,381,393,399,411,417,420,429,447,453,471,483,489,501
%N A243932 Positive integers with the same number of twin divisors as non-twin divisors.
%C A243932 A divisor m of n is twin if the positive values of m - 2 and/or m + 2 also divides n.
%C A243932 A divisor k of n is non-twin if the positive values of neither k - 2 nor k + 2 divide n.
%H A243932 Jens Kruse Andersen, <a href="/A243932/b243932.txt">Table of n, a(n) for n = 1..10000</a>
%F A243932 A243865(a(n)) = A243917(a(n)).
%e A243932 The divisors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. Of these, 2, 4, 8, 10, are twin divisors and 1, 5, 20, 40 are non-twin divisors. These are the same number of twin divisors (4) as non-twin divisors (4), so 40 is in this sequence.
%t A243932 fQ[n_] := Block[{d = Divisors@ n}, Length@ d == 2Length@ Select[d, MemberQ[d, # + 2] || MemberQ[d, # - 2] &]]; Select[ Range@ 520, fQ] (* _Robert G. Wilson v_, Jun 22 2014 *)
%o A243932 (PARI)
%o A243932 isOK(n) = t=sumdiv(n, d, (d>2 && n%(d-2)==0) || (d<=n-2 && n%(d+2)==0)); if(t==numdiv(n)-t, 1, 0)
%o A243932 s=[]; for(n=1, 600, if(isOK(n), s=concat(s, n))); s \\ _Colin Barker_, Jun 30 2014
%Y A243932 Cf. A134321, A243865, A243917.
%K A243932 nonn
%O A243932 1,1
%A A243932 _Juri-Stepan Gerasimov_, Jun 15 2014
%E A243932 Missing term (168) inserted by _Colin Barker_, Jun 30 2014