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A132882
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a(n) = the sum of the positive isolated divisors of n.
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5
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1, 0, 4, 4, 6, 6, 8, 12, 13, 15, 12, 18, 14, 21, 24, 28, 18, 33, 20, 30, 32, 33, 24, 50, 31, 39, 40, 53, 30, 55, 32, 60, 48, 51, 48, 81, 38, 57, 56, 78, 42, 77, 44, 81, 78, 69, 48, 114, 57, 90, 72, 95, 54, 114, 72, 102, 80, 87, 60, 147, 62, 93, 104, 124, 84, 138, 68, 123, 96
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OFFSET
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1,3
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COMMENTS
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A divisor, d, of n is isolated if neither (d-1) nor (d+1) divides n.
The convention for 1 is that it is an isolated divisor iff n is not even. - Olivier Gérard, Sep 22 2007
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LINKS
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FORMULA
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EXAMPLE
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The positive divisors of 56 are: 1,2,4,7,8,14,28,56. Of these, 1 and 2 are adjacent and 7 and 8 are adjacent. The isolated divisors are therefore 4,14, 28,56. So a(56) = 4 +14 +28 +56 = 102.
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MATHEMATICA
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Table[Plus@@Select[Divisors[n], (#==1||Mod[n, #-1]>0)&&Mod[n, #+1]>0&], {n, 1, 200}] (* Olivier Gérard, Sep 22 2007 *)
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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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