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A300717
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Möbius transform of A003557, n divided by its largest squarefree divisor.
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9
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1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6
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OFFSET
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1,8
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COMMENTS
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LINKS
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FORMULA
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Multiplicative with a(p) = 0 and a(p^e) = (p-1)*p^(e-2) for prime p and e>1. - Werner Schulte, Sep 27 2018
a(n) = Sum_{k=1..n} phi(gcd(n,k))*mu(gcd(n,k)).
a(n) = Sum_{k=1..n} phi(gcd(n,k))*mu(n/gcd(n,k)). (End)
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MAPLE
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with(numtheory): A003557 := n -> n/ilcm(op(numtheory[factorset](n))):
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MATHEMATICA
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Table[DivisorSum[n, MoebiusMu[#] EulerPhi[#] EulerPhi[n/#] &], {n, 108}] (* Michael De Vlieger, Nov 18 2019 *)
f[p_, e_] := If[e == 1, 0, (p - 1)*p^(e - 2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Dec 06 2022 *)
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PROG
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(PARI)
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0, f[i, 2]-1)); factorback(f); }; \\ From A003557
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] == 1, 0, (f[i, 1] - 1)*f[i, 1]^(f[i, 2] - 2))); } \\ Amiram Eldar, Dec 06 2022
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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