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A133944
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Sum mu(k), where the sum is over the integers k which are the "non-isolated divisors" of n and mu(k) is the Moebius function (mu(k) = A008683(k)). A positive divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.
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2
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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, -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, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0
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OFFSET
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1,132
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LINKS
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FORMULA
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MAPLE
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A133944 := 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 k-1 in divs or k+1 in divs then a := a+numtheory[mobius](k) ; fi ; od: RETURN(a) ; end: seq(A133944(n), n=1..120) ; # R. J. Mathar, Oct 21 2007
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PROG
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(PARI) A133944(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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