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A093318
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a(n) = number of positive divisors k of n where mu(k) = 1 and mu(n/k) = -1.
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1
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0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 4, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 4, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 4, 1, 1, 0, 4, 1, 0, 1, 0, 1, 1, 0, 4, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0
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OFFSET
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1,30
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LINKS
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FORMULA
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4*a(n) + Sum_{k|n} mu(k)*mu(n/k) = Product_{p|n} e(p, n), where the product is over the distinct primes dividing n; e(p, n) = 2 if p|n but p^2 does not divide n; e(p, n) = 1 if p^2|n but p^3 does not divide n; e(p, n) = 0 if p^3|n.
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MATHEMATICA
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a[n_] := DivisorSum[n, 1 &, MoebiusMu[#] == 1 && MoebiusMu[n/#] == -1 &]; Array[a, 100] (* Amiram Eldar, Aug 29 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 24 2004
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STATUS
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approved
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