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A134338
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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.
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1
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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; internal format)
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OFFSET
| 1,3
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COMMENTS
| 2 has no isolated divisors. So a(2) is 1.
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FORMULA
| a(2n-1) = A007955(2n-1); a(2n) = A007955(2n) / A134339(n). - Chandler
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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.
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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 (deutsch(AT)duke.poly.edu), Oct 24 2007
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MATHEMATICA
| f[n_]:=Module[{dn=Divisors[n]}, Complement[dn, Union[Flatten[Select[Partition[dn, 2, 1], #[[2]]-#[[1]]==1&]]]]]
Table[Times@@f[i], {i, 60}] [From Harvey P. Dale, Jan. 9, 2011]
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CROSSREFS
| Cf. A133779, A132881, A134339.
Sequence in context: A095138 A026475 A101747 * A084919 A153100 A143152
Adjacent sequences: A134335 A134336 A134337 * A134339 A134340 A134341
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Oct 21 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 24 2007
Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 24 2008
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