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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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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A133943(n) = -A133944(n), for n >= 2.
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 (rayjchandler(AT)sbcglobal.net), Jun 25 2008
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MAPLE
| 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 (mathar(AT)strw.leidenuniv.nl), Oct 21 2007
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CROSSREFS
| Cf. A133944.
Sequence in context: A014834 A015659 A132918 * A014084 A014159 A014184
Adjacent sequences: A133940 A133941 A133942 * A133944 A133945 A133946
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, Sep 30 2007, Oct 27 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 21 2007
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