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A131038
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a(1)=1. For n >=2, sum{k|n, neither (k+1) nor (k-1) divides n} a(k) = 0. (The sum is over 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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0
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1, 0, -1, 0, -1, 0, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, -1, 1, 1, -1, 0, 0, 1, 0, 0, -1, -2, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, -1, -2, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 1, -1, 1, 1, -1, 1, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 0, 1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, 1, 1, 1, 0, -1, 0, 0, 0, -1, -1, -1, 0, -1, 1, -1, 0, -1
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OFFSET
| 1,30
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COMMENTS
| The value of a(2) is arbitrary. If a(2) is any number and the rest of the sequence remains unchanged, then the sum over isolated divisors still always equals 0 for all n >= 2.
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EXAMPLE
| The positive divisors of 30 are 1,2,3,5,6,10,15,30. Of these, 1,2,3 are adjacent and 5 and 6 are adjacent. So the isolated divisors of 30 are 10,15,30. Therefore a(30) is such that a(10)+a(15)+a(30) = 1 +1 +a(30) =0. So a(30) = -2.
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CROSSREFS
| Cf. A008683.
Sequence in context: A048484 A016366 A016427 * A016353 A016398 A024359
Adjacent sequences: A131035 A131036 A131037 * A131039 A131040 A131041
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KEYWORD
| sign
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AUTHOR
| Leroy Quet, Sep 23 2007
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 25 2008
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