A134338 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.
1, 1, 3, 4, 5, 6, 7, 32, 27, 50, 11, 72, 13, 98, 225, 512, 17, 972, 19, 200, 441, 242, 23, 13824, 125, 338, 729, 10976, 29, 4500, 31, 16384, 1089, 578, 1225, 419904, 37, 722, 1521, 64000, 41, 12348, 43, 42592, 91125, 1058, 47, 10616832, 343, 62500, 2601
Offset: 1
Keywords
Examples
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.
Programs
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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: product(ISO[j],j=1..nops(ISO)) end proc: seq(a(n),n=1..50); # Emeric Deutsch, Oct 24 2007 -
Mathematica
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 *)
Formula
Extensions
More terms from Emeric Deutsch, Oct 24 2007
Extended by Ray Chandler, Jun 24 2008
Comments