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%I #19 Jan 10 2023 01:20:55
%S 0,0,0,0,0,-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,
%T 0,0,0,0,-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,
%U 0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,-1,0,-1,0,0,0,0,0,-1,0,0,0,-1,0,-1,0
%N Sum mu(k), where the sum is over the integers k which are the "non-isolated divisors" of n and mu(k) is the Moebius function (mu(k) = A008683(k)). A positive divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.
%H Antti Karttunen, <a href="/A133944/b133944.txt">Table of n, a(n) for n = 1..65537</a>
%F A133943(n) = -a(n), for n >= 2.
%p A133944 := 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 k-1 in divs or k+1 in divs then a := a+numtheory[mobius](k) ; fi ; od: RETURN(a) ; end: seq(A133944(n),n=1..120) ; # _R. J. Mathar_, Oct 21 2007
%o (PARI) A133944(n) = sumdiv(n,d,(!if((1==d),(n%2),(n%(d-1))&&(n%(d+1))))*moebius(d)); \\ _Antti Karttunen_, Sep 02 2018
%Y Cf. A133943.
%K sign
%O 1,132
%A _Leroy Quet_, Sep 30 2007
%E More terms from _R. J. Mathar_, Oct 21 2007