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A074722
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a(n) = Sum_{d divides n} phi(n/d)*(-1)^bigomega(d).
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4
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1, 0, 1, 2, 3, 0, 5, 2, 5, 0, 9, 2, 11, 0, 3, 6, 15, 0, 17, 6, 5, 0, 21, 2, 17, 0, 13, 10, 27, 0, 29, 10, 9, 0, 15, 10, 35, 0, 11, 6, 39, 0, 41, 18, 15, 0, 45, 6, 37, 0, 15, 22, 51, 0, 27, 10, 17, 0, 57, 6, 59, 0, 25, 22, 33, 0, 65, 30, 21, 0, 69, 10, 71, 0, 17, 34, 45, 0, 77, 18, 41, 0
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OFFSET
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1,4
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COMMENTS
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a(n) = 0 if and only if n == 2 (mod 4). - Robert Israel, Jan 04 2017
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LINKS
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FORMULA
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Multiplicative with a(p^e) = 2*(-1)^(e+1)*((-p)^(e+1)-1)/(p+1)-p^e.
a(n) = Sum_{k=1..n} (-1)^bigomega(gcd(n,k)). - Ilya Gutkovskiy, Feb 22 2020
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MAPLE
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f:= proc(n) uses numtheory; local d;
add(phi(n/d)*(-1)^bigomega(d), d=divisors(n))
end proc:
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MATHEMATICA
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f[d_] := EulerPhi[n/d] LiouvilleLambda[d]
f[p_, e_] := 2*(-1)^(e + 1)*((-p)^(e + 1) - 1)/(p + 1) - p^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 30 2022 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*(-1)^bigomega(d)); \\ Michel Marcus, Jul 11 2018
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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