OFFSET
1,1
COMMENTS
Obviously, all divisors of an odd number are isolated.
a(n) = 2*A112886(n). - Chandler
EXAMPLE
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.
MAPLE
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);
MATHEMATICA
Select[2*Range[120], Min[Differences[Rest[Divisors[#]]]]>1&] (* Harvey P. Dale, Jul 13 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Oct 16 2007, Oct 19 2007
EXTENSIONS
Corrected and extended by Ray Chandler, May 29 2008
STATUS
approved