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A369700
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Möbius transform of reduced totient function (A002322).
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0
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1, 0, 1, 1, 3, 0, 5, 0, 4, 0, 9, -1, 11, 0, -1, 2, 15, 0, 17, -1, -1, 0, 21, 0, 16, 0, 12, -1, 27, 0, 29, 4, -1, 0, 3, 0, 35, 0, -1, 0, 39, 0, 41, -1, 4, 0, 45, 0, 36, 0, -1, -1, 51, 0, 7, 0, -1, 0, 57, 1, 59, 0, -4, 8, -3, 0, 65, -1, -1, 0
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OFFSET
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1,5
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COMMENTS
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Since A002322(n) = A000010(n) for n = 1, 2, 4, and odd prime powers, a(n) = A007431(n) for the same values of n.
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LINKS
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FORMULA
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EXAMPLE
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a(8) = mu(1)*lambda(8) + mu(2)*lambda(4) + mu(4)*lambda(2) + mu(8)*lambda(1) = 0.
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MATHEMATICA
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a[n_] := DivisorSum[n, MoebiusMu[#] * CarmichaelLambda[n/#] &]; Array[a, 100] (* Amiram Eldar, Jan 29 2024 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, moebius(d)*lcm(znstar(n/d)[2]))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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