Search: id:A132895
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%I A132895
%S A132895 2,4,8,10,14,16,22,26,28,32,34,38,44,46,50,52,58,62,64,68,70,74,76,82,
%T A132895 86,88,92,94,98,104,106,116,118,122,124,128,130,134,136,142,146,148,152,
%U A132895 154,158,164,166,170,172,176,178,184,188,190,194,196,202,206,208,212
%N A132895 Even numbers for which all divisors, with the exception of 1 and 2, are 
               isolated. A positive divisor, k, of n is isolated if neither (k-1) 
               nor (k+1) divides n.
%C A132895 Obviously, all divisors of an odd number are isolated.
%C A132895 a(n) = 2*A112886(n). - Chandler
%e A132895 28 is a term of the sequence because its divisors are 1,2,4,7,14, 28 
               and only 1 and 2 are non-isolated. 30 does not belong to the sequence 
               because its divisors are 1,2,3,4,6,8,12, 24 and 1,2,3,4 are non-isolated.
%p A132895 with(numtheory): b:=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: 
               a:=proc(n) if nops(b(n))= tau(n)-2 then n else end if end proc: seq(a(n), 
               n=4..200);
%Y A132895 Cf. A112886, A133950, A133951, A088722-A088726.
%Y A132895 Sequence in context: A154115 A071703 A010069 this_sequence A125499 A153974 
               A034822
%Y A132895 Adjacent sequences: A132892 A132893 A132894 this_sequence A132896 A132897 
               A132898
%K A132895 nonn
%O A132895 1,1
%A A132895 Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 16 2007, Oct 19 2007
%E A132895 Corrected and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), 
               May 29 2008

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