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%I #18 Feb 15 2019 10:03:37
%S 1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,
%T 0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,
%U 0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0
%N Sum mu(k), where the sum is over the integers k which are the "isolated divisors" of n and mu(k) is the Moebius function (mu(k) = A008683(k)). A positive divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.
%C A133943(n) = -A133944(n), for n >= 2.
%C Is every term either 0 or 1?
%C No, a(132)=2, a(870)=3, a(8844)=4, a(420)=-1, a(1190)=-2, a(1260)=-3, a(7140)=-4. - _Ray Chandler_, Jun 25 2008
%C And a(14280) = -5. - _Antti Karttunen_, Sep 02 2018
%H Antti Karttunen, <a href="/A133943/b133943.txt">Table of n, a(n) for n = 1..65537</a>
%p A133943 := proc(n) local divs,k,i,a ; divs := convert(numtheory[divisors](n),list); a := 0 ; for i from 1 to nops(divs) do k := op(i,divs) ; if not k-1 in divs and not k+1 in divs then a := a+numtheory[mobius](k); fi ; od: RETURN(a) ; end: seq(A133943(n),n=1..120) ; # _R. J. Mathar_, Oct 21 2007
%o (PARI) A133943(n) = sumdiv(n,d,(!!if((1==d),(n%2),(n%(d-1))&&(n%(d+1))))*moebius(d)); \\ _Antti Karttunen_, Sep 02 2018
%Y Cf. A133944.
%K sign
%O 1,132
%A _Leroy Quet_, Sep 30 2007, Oct 27 2007
%E More terms from _R. J. Mathar_, Oct 21 2007
%E Secondary offset added by _Antti Karttunen_, Sep 02 2018
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