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%I #18 Feb 09 2014 22:44:34
%S 1,1,3,4,5,6,7,32,27,50,11,72,13,98,225,512,17,972,19,200,441,242,23,
%T 13824,125,338,729,10976,29,4500,31,16384,1089,578,1225,419904,37,722,
%U 1521,64000,41,12348,43,42592,91125,1058,47,10616832,343,62500,2601
%N a(n) = product of the "isolated divisors" of n. A divisor k of n is isolated if neither k-1 nor k+1 divides n.
%C 2 has no isolated divisors. So a(2) is 1.
%F a(2n-1) = A007955(2n-1); a(2n) = A007955(2n) / A134339(n). - _Ray Chandler_
%e The divisors of 20 are 1, 2, 4, 5, 10, 20. Of these, 10 and 20 are the isolated divisors. So a(20) = 10*20 = 200.
%p 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: product(ISO[j],j=1..nops(ISO)) end proc: seq(a(n),n=1..50); # _Emeric Deutsch_, Oct 24 2007
%t isoDivs[n_] := Module[{dn = Divisors[n]}, Complement[dn, Union[Flatten[Select[Partition[dn, 2, 1], #[[2]] - #[[1]] == 1 &]]]]]; Table[Times@@isoDivs[i], {i, 60}] (* _Harvey P. Dale_, Jan 09 2011 *)
%Y Cf. A133779, A132881, A134339.
%K nonn
%O 1,3
%A _Leroy Quet_, Oct 21 2007
%E More terms from _Emeric Deutsch_, Oct 24 2007
%E Extended by _Ray Chandler_, Jun 24 2008
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