This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A132881 #20 Aug 06 2025 03:34:22
%S A132881 1,0,2,1,2,1,2,2,3,2,2,2,2,2,4,3,2,3,2,2,4,2,2,4,3,2,4,4,2,3,2,4,4,2,
%T A132881 4,5,2,2,4,4,2,3,2,4,6,2,2,6,3,4,4,4,2,5,4,4,4,2,2,6,2,2,6,5,4,5,2,4,
%U A132881 4,6,2,6,2,2,6,4,4,5,2,6,5,2,2,6,4,2,4,6,2,5,4,4,4,2,4,8,2,4,6,5,2,5,2,6,8
%N A132881 a(n) is the number of isolated divisors of n.
%C A132881 A divisor d of n is isolated if neither d-1 nor d+1 divides n.
%C A132881 The convention for 1 is that it is an isolated divisor iff n is odd. - _Olivier Gérard_, Sep 22 2007
%H A132881 Ray Chandler, <a href="/A132881/b132881.txt">Table of n, a(n) for n=1..10000</a>
%F A132881 a(n) = A000005(n) - A132747(n).
%e A132881 The positive divisors of 56 are 1,2,4,7,8,14,28,56. Of these, 1 and 2 are adjacent and 7 and 8 are adjacent. The isolated divisors are therefore 4,14,28,56. There are 4 of these, so a(56) = 4.
%p A132881 with(numtheory): a:=proc(n) local div, ISO, i: div:=divisors(n): ISO:={}: for i to tau(n) do if member(div[i]-1, div)=false and member(div[i]+1, div)=false then ISO:=`union`(ISO,{div[i]}) end if end do end proc; 1, 0, seq(nops(a(j)), j=3..105); # _Emeric Deutsch_, Oct 02 2007
%t A132881 Table[Length@Select[Divisors[n],(#==1||Mod[n,#-1]>0)&&Mod[n,#+1]>0&],{n,1,200}] (* _Olivier Gérard_ Sep 22 2007 *)
%t A132881 id[n_]:=DivisorSigma[0,n]-Length[Union[Flatten[Select[Partition[Divisors[ n],2,1],#[[2]]-#[[1]]==1&]]]]; Array[id,110] (* _Harvey P. Dale_, Jun 04 2018 *)
%Y A132881 Cf. A132882, A132747.
%K A132881 nonn
%O A132881 1,3
%A A132881 _Leroy Quet_, Sep 03 2007
%E A132881 More terms from _Olivier Gérard_, Sep 22 2007