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 A131038 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.). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,30 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. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 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. PROG (PARI) A131038(n) = if(n<=2, 2-n, -((n%2)+sumdiv(n, d, if((d2)&&(n%(d-1))&&(n%(d+1)), A131038(d), 0)))); \\ Antti Karttunen, Apr 06 2021 CROSSREFS Cf. A008683, A132881. Sequence in context: A016427 A326170 A243841 * A016353 A016398 A024359 Adjacent sequences:  A131035 A131036 A131037 * A131039 A131040 A131041 KEYWORD sign,changed AUTHOR Leroy Quet, Sep 23 2007 EXTENSIONS Extended by Ray Chandler, Jun 25 2008 STATUS approved

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Last modified April 13 16:27 EDT 2021. Contains 342936 sequences. (Running on oeis4.)