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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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1
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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
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1,30
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COMMENTS
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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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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..65537
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EXAMPLE
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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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PROG
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(PARI) A131038(n) = if(n<=2, 2-n, -((n%2)+sumdiv(n, d, if((d<n)&&(d>2)&&(n%(d-1))&&(n%(d+1)), A131038(d), 0)))); \\ Antti Karttunen, Apr 06 2021
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CROSSREFS
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Cf. A008683, A132881.
Sequence in context: A016427 A326170 A243841 * A016353 A016398 A024359
Adjacent sequences: A131035 A131036 A131037 * A131039 A131040 A131041
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KEYWORD
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sign,changed
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AUTHOR
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Leroy Quet, Sep 23 2007
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EXTENSIONS
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Extended by Ray Chandler, Jun 25 2008
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STATUS
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approved
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