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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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

2 has no isolated divisors. So a(2) is 1.

LINKS

Table of n, a(n) for n=1..51.

FORMULA

a(2n-1) = A007955(2n-1); a(2n) = A007955(2n) / A134339(n). - Ray Chandler

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A133779, A132881, A134339.

Sequence in context: A095138 A026475 A101747 * A084919 A153100 A143152

Adjacent sequences:  A134335 A134336 A134337 * A134339 A134340 A134341

KEYWORD

nonn

AUTHOR

Leroy Quet, Oct 21 2007

EXTENSIONS

More terms from Emeric Deutsch, Oct 24 2007

Extended by Ray Chandler, Jun 24 2008

STATUS

approved

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Last modified March 25 01:17 EDT 2019. Contains 321450 sequences. (Running on oeis4.)