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%I #8 Jul 13 2022 13:27:15
%S 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 86,88,92,94,98,104,106,116,118,122,124,128,130,134,136,142,146,148,
%U 152,154,158,164,166,170,172,176,178,184,188,190,194,196,202,206,208,212
%N 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 Obviously, all divisors of an odd number are isolated.
%C a(n) = 2*A112886(n). - Chandler
%e 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 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);
%t Select[2*Range[120],Min[Differences[Rest[Divisors[#]]]]>1&] (* _Harvey P. Dale_, Jul 13 2022 *)
%Y Cf. A112886, A133950, A133951, A088722-A088726.
%K nonn
%O 1,1
%A _Emeric Deutsch_, Oct 16 2007, Oct 19 2007
%E Corrected and extended by _Ray Chandler_, May 29 2008
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