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A243917
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Number of non-twin divisors of n.
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6
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1, 2, 0, 1, 2, 2, 2, 2, 1, 4, 2, 1, 2, 4, 1, 3, 2, 4, 2, 4, 2, 4, 2, 2, 3, 4, 2, 4, 2, 5, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 6, 2, 4, 3, 4, 2, 4, 3, 6, 2, 4, 2, 6, 4, 6, 2, 4, 2, 4, 2, 4, 2, 5, 4, 6, 2, 4, 2, 6, 2, 6, 2, 4, 3, 4, 4, 6, 2, 6, 3, 4, 2, 5, 4, 4, 2, 6, 2, 9, 4, 4, 2, 4, 4, 6
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OFFSET
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1,2
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COMMENTS
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A divisor k of n is non-twin if neither the positive values of k - 2 nor k + 2 divide n.
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LINKS
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FORMULA
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EXAMPLE
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The positive divisors of 12 are: 1, 2, 3, 4, 6, 12. Of these, 1 and 3 are twin divisors, 2, 4 and 6 are also twin divisors. The unique non-twin divisor is therefore 12. So a(12) = the number of these divisors, which is 1.
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MATHEMATICA
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a243917[n_Integer] := Length[Select[Divisors[n], If[And[# <= 2 || Divisible[n, # - 2] == False, Divisible[n, # + 2] == False], True, False] &]]; a243917 /@ Range[120] (* Michael De Vlieger, Aug 17 2014 *)
nntd[n_]:=Module[{d=Select[Divisors[n], #>2&], t}, t=Count[d, _?(!Divisible[ n, #-2] && !Divisible[ n, #+2]&)]; If[!Divisible[ n, 3], t++]; If[ Divisible[ n, 2] && !Divisible[n, 4], t++]; t]; Array[nntd, 100] (* Harvey P. Dale, May 27 2016 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, (((d<=2) || (n % (d-2))) && (n % (d+2)))); \\ Michel Marcus, Jun 25 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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