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A133943
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Sum mu(k), where the sum is over the integers k which are the "isolated divisors" of n and mu(k) is the Moebius function (mu(k) = A008683(k)). A positive divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.
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2
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1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0
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OFFSET
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1,132
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COMMENTS
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Is every term either 0 or 1?
No, a(132)=2, a(870)=3, a(8844)=4, a(420)=-1, a(1190)=-2, a(1260)=-3, a(7140)=-4. - Ray Chandler, Jun 25 2008
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LINKS
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MAPLE
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A133943 := proc(n) local divs, k, i, a ; divs := convert(numtheory[divisors](n), list); a := 0 ; for i from 1 to nops(divs) do k := op(i, divs) ; if not k-1 in divs and not k+1 in divs then a := a+numtheory[mobius](k); fi ; od: RETURN(a) ; end: seq(A133943(n), n=1..120) ; # R. J. Mathar, Oct 21 2007
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PROG
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(PARI) A133943(n) = sumdiv(n, d, (!!if((1==d), (n%2), (n%(d-1))&&(n%(d+1))))*moebius(d)); \\ Antti Karttunen, Sep 02 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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