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 A132881 a(n) is the number of isolated divisors of n. 14
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A divisor d of n is isolated if neither d-1 nor d+1 divides n. The convention for 1 is that it is an isolated divisor iff n is odd. - Olivier Gérard, Sep 22 2007 LINKS Ray Chandler, Table of n, a(n) for n=1..10000 FORMULA a(n) = A000005(n) - A132747(n). EXAMPLE 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. MAPLE 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 MATHEMATICA Table[Length@Select[Divisors[n], (#==1||Mod[n, #-1]>0)&&Mod[n, #+1]>0&], {n, 1, 200}] - Olivier Gérard Sep 22 2007. 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 *) CROSSREFS Cf. A132882, A132747. Sequence in context: A178771 A289498 A193929 * A224702 A267263 A060130 Adjacent sequences:  A132878 A132879 A132880 * A132882 A132883 A132884 KEYWORD nonn AUTHOR Leroy Quet, Sep 03 2007 EXTENSIONS More terms from Olivier Gérard, Sep 22 2007 STATUS approved

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Last modified December 14 15:08 EST 2019. Contains 329979 sequences. (Running on oeis4.)