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A074823
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a(n) = 2^omega(n)*mu(n)^2.
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10
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1, 2, 2, 0, 2, 4, 2, 0, 0, 4, 2, 0, 2, 4, 4, 0, 2, 0, 2, 0, 4, 4, 2, 0, 0, 4, 0, 0, 2, 8, 2, 0, 4, 4, 4, 0, 2, 4, 4, 0, 2, 8, 2, 0, 0, 4, 2, 0, 0, 0, 4, 0, 2, 0, 4, 0, 4, 4, 2, 0, 2, 4, 0, 0, 4, 8, 2, 0, 4, 8, 2, 0, 2, 4, 0, 0, 4, 8, 2, 0, 0, 4, 2, 0, 4, 4, 4, 0, 2, 0, 4, 0, 4, 4, 4, 0, 2, 0, 0, 0, 2, 8, 2, 0, 8
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OFFSET
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1,2
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LINKS
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FORMULA
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Multiplicative with a(p)=2, a(p^e)=0, e > 1.
Sum_{n>0} a(n)/n^s = Product_{p prime} (1 + 2p^(-s)). - Ralf Stephan, Jul 07 2013
Dirichlet g.f.: zeta(s)^2 * Product_{primes p} (1 - 3/p^(2*s) + 2/p^(3*s)). - Vaclav Kotesovec, Aug 20 2021
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MATHEMATICA
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Table[MoebiusMu[n]^2 * 2^PrimeNu[n], {n, 1, 100}] (* Vaclav Kotesovec, Aug 20 2021 *)
f[p_, e_] :=If[e==1, 2, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jun 26 2022 *)
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PROG
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(PARI) a(n) = 2^omega(n)*moebius(n)^2; \\ Michel Marcus, Jul 23 2017
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 + 2*X))[n], ", ")) \\ Vaclav Kotesovec, Aug 20 2021
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - 3*X^2 + 2*X^3)/(1 - X)^2)[n], ", ")) \\ Vaclav Kotesovec, Aug 20 2021
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CROSSREFS
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KEYWORD
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mult,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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